3. A yard plan includes a rectangular garden that is surrounded by bricks. In the drawing, the garden is 7 inches
by 4 inches. The length and width of the actual garden will be 35 times larger than the length and width in the
drawing.
(a) What is the perimeter of the drawing? Show your work.
(b) What is the perimeter of the actual garden? Show your work.
(c) What is the effect on the perimeter of the garden with the dimensions are multiplied by 35? Show
your work.

The volume of the object is 168.96 cubic units. The volume of the object can be found using the formula for volume of a solid with known cross-sections : [tex]V = ∫ A(x)dx[/tex], where [tex]A(x)[/tex] is the area of the cross-section at x.

In this case, the cross-sections are triangles with equal base and height. The area of a triangle is A = 1/2bh, so the area of the cross-section at x is [tex]A(x) = 1/2b^2.[/tex]

The base of the triangle is the distance between the two curves, which is [tex]6−3/8 x^2 - 0 = 6−3/8 x^2.[/tex] So the area of the cross-section is [tex]A(x) = 1/2(6−3/8 x^2)^2.[/tex]

Now we can find the volume by integrating the area function over the x-values of the base region. The base region is bounded by the curve [tex]y=6−3/8 x^2[/tex], so the x-values are the roots of this equation:

[tex]0 = 6−3/8 x^2 3/8 x^2 = 6 x^2 = 16 x = ±4[/tex]

So the volume is:

[tex]V = ∫[−4,4] 1/2(6−3/8 x^2)^2dx = 1/2 ∫[−4,4] (36 - 9/4 x^2 + 9/64 x^4)dx[/tex]
[tex]= 1/2 [(36x - 3/4 x^3 + 9/320 x^5)] from x=-4 to x=4 = 1/2 [(288 - 192 + 72.96) - (-288 + 192 - 72.96)] = 1/2 (576 - 384 + 145.92) = 1/2 (337.92)[/tex]
= 168.96 , So the volume of the object is 168.96 cubic units.

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The two solutions of the equation x2 - 4x + 1 = 0 are x = 2 + √3 and x = 2 - √3.

A quadratic equation is an equation that can be written in the form ax2 + bx + c = 0, where a, b, and c are real numbers and a is not equal to 0. Solving a quadratic equation involves finding the value of x that makes the equation true. This can be done in multiple ways, but the most common method is to use the Quadratic Formula. The Quadratic Formula states that the roots (or solutions) of a quadratic equation can be found using the following formula:

x = [-b ± √(b2 - 4ac)]/2a

For example, consider the equation x2 - 4x + 1 = 0. In this equation, a = 1, b = -4, and c = 1. Plugging these values into the Quadratic Formula gives us:

x = [-(-4) ± √((-4)2 - 4(1)(1))]/2(1)

Simplifying this equation, we get:

x = [4 ± √(16 - 4)]/2

Finally, simplifying further yields the following two solutions:

x = (4 ± √12) /2

x = 2 ±√3

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1 to power 8 multiplied by 3 to power 0 multiplied 5 to the power of 3 multiplied 2 to the power of 2 is written as 1⁸ × 3⁰ × 5³ × 2² = 500

How many times an integer should be multiplied depends on its power (or exponent). It appears as a tiny number above and to the right of the main number.

How many times you should multiply an integer depends on its magnitude. Other terms for powers include exponents and indices.

Given,

1 to power 8 multiplied by 3 to power 0 multiplied 5 to the power of 3 multiplied 2 to the power of 2

That is written as 1⁸ × 3⁰ × 5³ × 2²

1⁸ × 3⁰ × 5³ × 2²

= 1 × 1 × 125 × 4

= 500

Hence the value of the equation is 500.

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The required mean of the given numbers in Exhibit 1.1 is 2.625.

To find the mean of the given numbers in Exhibit 1.1, we will use the following formula:

Mean = (Sum of all numbers) / (Total number of numbers)

Explanation:

Given data in the form of an exhibit is shown below Exhibit 1.1181310161413171513111414111012121113159121316815

Now, we will add all these numbers and find their sum.1 + 1 + 8 + 1 + 3 + 1 + 0 + 1 + 6 + 1 + 4 + 1 + 3 + 1 + 7 + 1 + 5 + 1 + 3 + 1 + 1 + 1 + 4 + 1 + 1 + 0 + 1 + 2 + 1 + 2 + 1 + 1 + 3 + 1 + 5 + 9 + 1 + 2 + 1 + 3 + 1 + 6 + 8 + 1 + 5= 105

Now, we will count the total number of numbers. There are 40 numbers in total. Therefore, the mean of the given numbers in Exhibit 1.1 is:

Mean = (Sum of all numbers) / (Total number of numbers)= 105 / 40= 2.625

Hence, the required mean of the given numbers in Exhibit 1.1 is 2.625.

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The rate of the selling price of each egg is 6%

The selling price of a commodity is the price at which a seller offers a product or service for sale to a buyer. It is the amount of money that a buyer must pay to purchase the commodity from the seller.

To calculate the selling price of a commodity, a seller typically adds a markup to the cost of production, which includes the direct and indirect costs of producing the commodity, such as materials, labor, and overhead expenses.

The markup is usually expressed as a percentage of the cost of production, and it varies depending on the industry, product, and market conditions.

If 200 eggs were bought for Rs10 each, then all egg costs Rs2000.

20 broken eggs, remaining 180 eggs.

Based on these conditions, we can formulate an equation:

10 × (8% + 1) ÷ (200 - 20)

Simplify;

[tex]=\dfrac{10\times 1.08}{180}[/tex]

Eliminate the common factor;

[tex]=\dfrac{1.08}{18}[/tex]

[tex]=\dfrac{108}{1800}[/tex]

Calculate the product or quotient;

[tex]=\dfrac{6}{100}[/tex]

Rewrite the rate of the selling price as a percentage = 6%

Therefore, we can conclude that the rate of the selling price as a percentage is 6%.

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The calculated value of x given that the streets are parallel to each other is 4760 feet

Given that the street are parallel to each other

We have the following equivalent ratio that can be used to calculate x

x : 2640 = 2380 : 1320

Express the ratio as fraction

So, the above ratio becomes the following equation

x / 2640 = 2380 / 1320

Solving further, we multiply both sides of the equation by 2640

So, we have

2640 * x / 2640 = 2380 / 1320 * 2640

Evaluate the products

x = 4760

Hence, the value of x is 4760 ft

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The probability of Roger selling a zucchini bread as the next loaf is 4/21.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

The probability of Roger selling a zucchini bread as the next loaf can be found by dividing the number of zucchini breads sold by the total number of breads sold so far.

The total number of breads sold so far is:

11 (banana) + 8 (zucchini) + 9 (cranberry) + 14 (blueberry) = 42

The number of zucchini breads sold is 8.

So the probability that the next loaf Roger sells will be zucchini bread is:

8/42 = 4/21

Therefore, the probability of Roger selling a zucchini bread as the next loaf is 4/21.

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Por lo tanto, la probabilidad de que ocurra al menos uno de los dos eventos en el juego es de 0,55 o 55%.

Podemos utilizar la regla de adición de probabilidades para calcular la probabilidad de que ocurra al menos uno de los dos eventos en el juego.

La regla de adición establece que la probabilidad de que ocurra al menos uno de dos eventos A o B es igual a la suma de las probabilidades de los eventos individuales menos la probabilidad de que ambos eventos ocurran juntos:

P(A o B) = P(A) + P(B) - P(A y B)

Podemos reemplazar los valores que se nos dan en la fórmula:

P(A o B) = 0,25 + 0,6 - 0,3

P(A o B) = 0,55

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The total length of the blue and pink yarn is 31 5/7  yards

The blue yarn is given as

Blue = 5 2/7 yards

The length of the pink yarn is 5 times the length of the blue yarn:

So, we have

Length of pink yarn = 5 x 5 2/7 yards

Length of pink yarn = 26 3/7 yards

To find the total length of the blue and pink yarn, we can add their lengths:

Total length = Length of blue yarn + Length of pink yarn

Total length = 5 2/7 yards + 26 3/7 yards

The fractions have the same denominator

So, we have

Total length = 31 5/7

Therefore, the total length of the blue and pink yarn is 31 5/7  yards

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The correct statements about the transformation are the shape of the parallelogram is preserved and the size of the parallelogram is changed.

The rule (x,y) ↛ ((2x+2y-4) represents a linear transformation that involves scaling and translating the coordinates of each point. Specifically, the transformation scales the x-coordinate by a factor of 2 and the y-coordinate by a factor of 2, and then translates the resulting coordinates 4 units to the right and 4 units down.

Based on this, we can make the following observations:

The shape of the parallelogram L'm'n'p is preserved under the transformation. That is, the transformed parallelogram LMNP is also a parallelogram.

The size of the parallelogram L'm'n'p is changed under the transformation. Specifically, the dimensions of the transformed parallelogram LMNP are twice as large as those of the original parallelogram L'm'n'p.

Therefore, the correct statements about the transformation are:

The shape of the parallelogram is preserved.

The size of the parallelogram is changed.

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The probability of having a type 2 defect given a type 1 defect is 0.6667, rounded to four decimal places.

The probability of having a type 2 defect given a type 1 defect is the conditional probability of having a type 2 defect given a type 1 defect divided by the probability  . This can be expressed as P(type 2 defect|type 1 defect)/P(type 1 defect).

P(type 2 defect|type 1 defect) = 0.2

P(type 1 defect) = 0.3

Therefore,

P(type 2 defect|type 1 defect) / P(type 1 defect) = 0.2 / 0.3 = 0.6667

The probability of having a type 2 defect given a type 1 defect is 0.6667 and when rounded to four decimal places it is 0.6667.

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As per the concept of compound interest, the total amount of money needed to pay back the loan in 3 years is $6,035.50.

Now, let's move on to the problem. You are given that $5,000 is borrowed with an interest of 12.3% compounded semi-annually. This means that the interest rate of 12.3% is divided by 2 to get the semi-annual interest rate, which is 6.15% (12.3% / 2). The interest is compounded twice a year, so there will be 6 months between each compounding period.

To find the total amount of money needed to pay back the loan in 3 years, we need to use the formula for compound interest:

A = P(1 + r/n)ⁿˣ

where:

A = the total amount of money needed to pay back the loan

P = the principal amount borrowed

r = the annual interest rate (in decimal form)

n = the number of times the interest is compounded per year

x = the number of years

In this case, we have:

P = $5,000

r = 12.3% = 0.123

n = 2 (compounded semi-annually)

x = 3 years

So the formula becomes:

A = $5,000(1 + 0.0615/2)²ˣ³

Simplifying this, we get:

A = $5,000(1.03075)⁶

Using a calculator, we can find that 1.03075 raised to the power of 6 is approximately 1.2071. So:

A = $5,000(1.2071)

A = $6,035.50

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Answer:

  2,420,000 m³

Step-by-step explanation:

You want the volume of a square pyramid 220 m on a side and 150 m high.

The volume of a pyramid is 1/3 the volume of a cuboid of the same dimensions.

  V = 1/3LWH

  V = 1/3(220 m)²(150 m) = 2420000 m³

The volume of the pyramid is about 2,420,000 cubic meters.

__

Additional comment

The density of Egyptian limestone is between 2.4 and 2.7 g/cm³, so the mass of the pyramid is approximately 6 million metric tons. This is about 50% more than the most massive building built in modern times.

There are 10 rulers when there are 20 students. The problem involves using an equation to relate the number of rulers and students.

The problem describes a relationship between the number of rulers and the number of students, where the number of rulers is five more than one-fourth of the number of students. To find the number of rulers when there are 20 students, we can use the equation:

r = (1/4)s + 5

where "r" is the number of rulers and "s" is the number of students. Substituting s = 20, we get:

r = (1/4)(20) + 5

r = 10

Therefore, there are 10 rulers when there are 20 students.

In summary, the problem involves using an equation to relate the number of rulers and students. To solve the problem, we substitute the given value for the number of students into the equation and solve for the number of rulers.

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The complete question is :

There are five more rulers than a fourth of the number of the students. Find number of rulers when there are 20 students?

Answer:

8

Step-by-step explanation:

40% is 4 times 10%, so the number is 4 times greater.

4 × 2 = 8

Answer: 8

Let's call the number we're trying to find "x".

We know that 10% of x is equal to 2.

So, we can set up the equation:

0.1x = 2

To solve for x, we can divide both sides by 0.1:

x = 2 ÷ 0.1

x = 20

Now that we know x is 20, we can find 40% of that number:

40% of 20 = 0.4 x 20 = 8

Therefore, 40% of that number is equal to 8.

Answer:

length of base = 17 cm

Step-by-step explanation:

Area of a triangle A = 1/2 bh where b = base h = height

We are given
b = 2h - 7

A = 102

or
2h = b + 7

h = (b+7) /2

use this in the equation for A

1/2 (b) (b+7)/2 = 102

1/4 x b(b+7) = 102

b(b+7) = 4 x 102

b² + 7 b = 408

b² + 7b - 408 = 0

This is a quadratic equation which can be solved by factoring or using the quadratic formula

We can factor b² + 7b - 408 as follows

Check if b = 17 is correct

With b = 17

h = (b+7) /2

= (17 + 7)/2

= 24/2

= 12

Therefore A = 1/2 x 17 x 12

= 17 x 6

= 102

Hence, in answering the stated question, we may say that As a result, the  expressions value of P75 is 80.375.

In mathematics, you can multiply, divide, add, or subtract. An expression is formed as follows: Expression, number, and math operator Numbers, parameters, and functions make up a mathematical expression. It is possible to contrast phrases and expressions. Every mathematical statement that contains variables, numbers, and a mathematical action between them is referred to as an expression. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the provided equation, all separated by the mathematical sign +.

To determine the value of P75, or the 75th percentile, we must first determine the score at which 75% of the scores fall.

z = (x - μ) / σ

where x is the score to be converted, the mean, and the standard deviation.

As a result, we can write:

0.75 = P(Z ≤ 0.675)

where Z is the mean of the standard normal variable and the standard deviation is 1.

Now we can rearrange the z-score calculation to find the score x:

x = μ + zσ

Using the values we have:

x = 77.4 + (0.675)(5) (5)

x = 80.375

As a result, the value of P75 is 80.375.

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Therefore, the minimum score required for the scholarship 652

We are told in the question that:

A university plans to award scholarships to students whose scores are in the top 30%.

The top 30% means

100 - 30% = 70%

This means the student must be in the 93rd percentile

We solve using the z-score formula.

z = (x-μ)/σ, where

x is the raw score?

μ is the population mean = 496

σ is the population standard deviation = 109

Z score for 93rd percentile = 1.476

1.476 = x - 491/109

Cross Multiply

1.476 × 109 = x - 491

160.884 = x - 491

x = 160.884 + 491

x = 651.884

Approximately to the nearest whole number = 652

Therefore, the minimum score required for the scholarship 652

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The values of x and y that satisfy the system of equations are x = 5 and y = -2.

To solve these equations simultaneously, we can use the method of substitution.

First, let's solve one of the equations for one of the variables. We can rearrange the first equation to solve for x:

2x + 3y = 4

2x = 4 - 3y

x = (4 - 3y)/2

Now we can substitute this expression for x into the second equation and solve for y:

-6y - 2x = 2

-6y - 2((4-3y)/2) = 2

-6y - 4 + 3y = 2

-3y = 6

y = -2

We have found that y = -2. We can now substitute this value back into either of the original equations to solve for x. Let's use the first equation:

2x + 3y = 4

2x + 3(-2) = 4

2x = 10

x = 5

Therefore, the solution to the system of equations is x = 5 and y = -2.

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Therefore, the correct answer is B: "This is not a function because one input has two different outputs."

A mapping diagram is a graphical representation of a function that shows how elements of one set are mapped or transformed into elements of another set. It consists of two columns or sets, the first one is the input set, and the second one is the output set. The mapping rule or function is applied to each element of the input set to obtain the corresponding element of the output set. The elements of the input set are typically represented as points or values on the left-hand side, while the corresponding elements of the output set are represented as points or values on the right-hand side. Mapping diagrams are often used to illustrate simple functions, such as those involving basic arithmetic operations or algebraic expressions. They can also be used to demonstrate the properties of more complex functions, such as those involving trigonometric or exponential functions.

Here,

A mapping diagram is a visual representation of a relation between two sets of numbers, where each input corresponds to an output. In this diagram, we can see that each input (represented in the left column) has only one corresponding output (represented in the right column), except for the number 10, which has two outputs, 3 and 7. This violates the definition of a function, which states that each input can have only one output.

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Since Mehrine and Zaara both brought equal amount of money for shopping, Mehrine brought Rs. 5000 for shopping.

What are Linear equations?

Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line.

Let the equal amount of money they both brought = x

Mehrine spent Rs 500 on a pair of shoes, therefore, the money Mehrine has left

= x-500

Zaara bought a dress for Rs 2000, therefore, the money Zaara has left

= x-2000

Zaara has ⅔ of what Mehrine had left.

Therefore:

[tex]x - 2000 = \frac{2}{3}(x - 500)[/tex]

Cross multiply

3(x - 2000) = 2(x - 500)

3x - 6000 = 2x - 1000

3x - 2x = 6000 - 1000

x=5000

Therefore, Mehrine brought Rs5000 for shopping.

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The area of the sector is π square meters.

Length of arc [tex]= (90/360)* 2π(2m) = πm[/tex]

To find the area of the sector and the length of the arc, we need to use the formulas:

Area of sector = ( Θ/360 x π[tex]r^2[/tex]

Length of arc = (θ/360) x 2πr

Given radius (r) = 2m and angle (θ) = 90 degrees, we can plug these values into the formulas to get:

Area of sector = [tex](90/360) * \pi (2m)^2[/tex]

[tex]= (1/4) * \pi * 4m^2[/tex]

[tex]= \pi m^2[/tex]

Therefore, the area of the sector is π square meters.

Length of arc = (90/360) x 2π(2m)

= (1/4) x 4πm

= πm

Therefore, the length of the arc is π meters.

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Step-by-step explanation:

Calculate 3/1 x 5/12 = 15/12

The denominator is constant, 12. Think of numbers that multiply the numerator.

What do you multiply by 1/12 to get 15/12?

Ans 15

What do you multiply by 3/12 to get 15/12

Ans 5

The equation of the line perpendicular to y = -4x - 2 and passing through (-12, 2) is y = 1/4x + 5.

Given that a line passes through (-12, 2) and is perpendicular to y = -4x - 2. We have to find the equation of this line. To find the equation of the line perpendicular to the given line, we need to know the slope of the line we want to find. The slope of the given line is -4. Since the lines are perpendicular, the slope of the line we want to find will be the negative reciprocal of -4, which is 1/4.

Thus, the equation of the line passing through (-12, 2) and is perpendicular to y = -4x - 2 is:y - 2 = 1/4(x + 12)Simplify by distributing the 1/4:y - 2 = 1/4x + 3

Add 2 to both sides: y = 1/4x + 5

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Answer:

from the figure

tanx= p/b

or, tanx= 4/9

or, x=arctan(4/9)

or, x=23.49°

The side lengths and the angle measures is PQ = 2, PR ≈ 3.61, QR = 3

m∠P = 90°, m∠Q = 90°, m∠R ≈ 33.7°

Tο find the side lengths, we need tο use the distance fοrmula:

PQ = √[(x₂ - x₁)² + (y₂ - y₁)²]

PR = √[(x₃ - x₁)² + (y₃ - y₁)²]

QR = √[(x₃ - x₂)² + (y₃ - y₂)²]

PQ = √[(-4 - (-2))² + (4 - 4)²] = √[2²] = 2

PR = √[(-4 - (-2))² + (1 - 4)²] = √[2² + 3²] = √13 ≈ 3.61

QR = √[(-4 - (-4))² + (1 - 4)²] = √[3²] = 3

Tο find the angle measures, we can use the Law οf Cοsines:

cοs(θ) = (b² + c² - a²) / 2bc

where a, b, and c are the side lengths οppοsite tο the cοrrespοnding angles. Fοr example, the angle measure at vertex P is οppοsite tο side PQ, sο we can use the lengths PR and QR tο find its angle measure.

cοs(m∠P) = (PR² + QR² - PQ²) / 2PRQR

cοs(m∠P) = (13 + 9 - 4) / (2 * √13 * 3)

cοs(m∠P) = 18 / (2√39)

m∠P = cοs⁻¹(18 / (2√39)) ≈ 90°

cοs(m∠Q) = (PQ² + QR² - PR²) / 2PQQR

cοs(m∠Q) = (4 + 9 - 13) / (2 * 2 * 3)

cοs(m∠Q) = 0

m∠Q = cοs⁻¹(0) = 90°

cοs(m∠R) = (PQ² + PR² - QR²) / 2PQPR

cοs(m∠R) = (4 + 16 - 13) / (2 * 2 * √13)

cοs(m∠R) = 7 / (4√13)

m∠R = cοs⁻¹(7 / (4√13)) ≈ 33.7°

Therefοre, the answer is:

PQ = 2, PR ≈ 3.61, QR = 3

m∠P = 90°, m∠Q = 90°, m∠R ≈ 33.7°

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a) The average daily balance for the billing period is $285.29.

b) The finance charge to be paid on February 13 is $3.42.

c) The balance due on February 13 is $288.71.

To calculate the average daily balance, we need to determine the daily balances for each day in the billing period. To do this, we need to add the previous day's balance to any new charges and subtract any payments or credits.

Day         Transaction       Daily Balance

Jan 13 Starting balance $221.33

Jan 17 Charge of $50 $271.33

Jan 22 Payment of $100 $171.33

Feb 4 Charge of $100 $271.33

Feb 6 Charge of $100 $371.33

Feb 10 Payment of $100 $271.33

Feb 13 Finance charge $288.71

To calculate the average daily balance, we add up the daily balances and divide by the number of days in the billing period:

To calculate the finance charge, we multiply the average daily balance by the interest rate and the number of days in the billing period:

To calculate the balance due on February 13, we add the finance charge to the average daily balance:

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The volume of cone in terms of π is 12π in³. The height of the given cone is 4.

The quantity of space a three-dimensional item occupies is measured by its volume. Usually, it is expressed in terms of cubic units like cubic metres (m³) or cubic millimetres (cm³).

We are given that the radius of the cone is 3 in and the slant height is 5 in. We need to find the height of the cone before we can calculate its volume.

        h² + r² = y²

        h² + 3² = 5²

        h² + 9 = 25

        h² = 16

        h = 4

        V = (1/3)πr²h

        V = (1/3)π(3²)(4)

        V = (1/3)π(9)(4)

        V = (1/3)(36π)

        V = 12π in³

Therefore, the volume of the cone in terms of π is 12π in³

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