Calculating the length of an edge of a prism - GMAT Quantitative

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Question

A new fish tank at a theme park must hold 450,000 gallons of sea water. Its dimensions must be such that it is twice as long as it is wide, and half as high as it is wide. If one gallon of water occupies 0.1337 cubic feet, then give the surface area of the proposed tank to the nearest square foot.

You may assume that the tank has all four sides and a bottom, but is open at the top.

Answer

450,000 gallons of water occupy $\small \small 0.1337 \cdot 450,000 \approx 60,165$ cubic feet.

Let $\small h$ be the height of the tank. Then the width of the tank is , and its length is . Multiply the dimensions to get the volume:

$V = LWH = H \cdot 2H\cdot 4H = 8H^{3} = 60,165$

$H^{3} = 60,165 \div 8 \approx 7,521$

$H = \sqrt[3]{7,521} \approx 19.6$

$W = 2H = 2 \cdot19.6 = 39.2$

$L = 2W = 2\cdot 39.2 = 78.4$

Since the tank has four sides and a bottom, but not a top, its surface area is

$A = 2\cdot 78.4\cdot 19.6 + 2\cdot 39.2\cdot 19.6 + 78.4\cdot 39.2$

$A = 2\cdot 78.4\cdot 19.6 + 2\cdot 39.2\cdot 19.6 + 78.4\cdot 39.2 \approx 7,683$

The surface area of the tank is about 7,683 square feet.

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Question

A rectangular prism has a volume of . If the length of the prism is and its width is , what is its height?

Answer

The volume of a rectangular prism is equal to its length times its width times its height. We are given the volume, the length, and the width, so using the following formula we can solve for the height of the rectangular prism:

$H=\frac{105}{35}=3$

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Question

Jenny wants to make a cube out of sheet metal. What is the length of one side of the cube?

I) The cube will require square inches of material.

II) The cube will hold cubic inches.

Answer

The length of an edge of a cube can be used to find either volume or surface area, and vice versa.

I) Gives us the surface area thus, we are able to calculate the length of an edge using the formula,

$SA=6\cdot s^2$

$294=6s^2 \rightarrow 49=s^2 \rightarrow 7=s$ .

II) Gives us the volume thus, we are able to calculate the length of an edge using the formula,

$343=s^3 \rightarrow 7=s$

Either can be used to find the side length.

Compare your answer with the correct one above

Question

A rectangular prism has a volume of , a length of , and a height of . What is the width of the prism?

Answer

Using the formula for the volume of a rectangular prism, we can plug in the given values and solve for the width of the prism:

$W=\frac{70}{14}=5$

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Question

A rectangular prism has a surface area of , a width of , and a height of . What is the length of the prism?

Answer

We are given the surface area and the length of two sides, so in order to calculate the length of the third side we need the formula for the surface area of a prism in terms of each side length:

Using the formula, we can simply plug in the given values and solve for the length of the rectangular prism:

Compare your answer with the correct one above

Question

A new fish tank at a theme park must hold 450,000 gallons of sea water. Its dimensions must be such that it is twice as long as it is wide, and half as high as it is wide. If one gallon of water occupies 0.1337 cubic feet, then give the surface area of the proposed tank to the nearest square foot.

You may assume that the tank has all four sides and a bottom, but is open at the top.

Answer

450,000 gallons of water occupy $\small \small 0.1337 \cdot 450,000 \approx 60,165$ cubic feet.

Let $\small h$ be the height of the tank. Then the width of the tank is , and its length is . Multiply the dimensions to get the volume:

$V = LWH = H \cdot 2H\cdot 4H = 8H^{3} = 60,165$

$H^{3} = 60,165 \div 8 \approx 7,521$

$H = \sqrt[3]{7,521} \approx 19.6$

$W = 2H = 2 \cdot19.6 = 39.2$

$L = 2W = 2\cdot 39.2 = 78.4$

Since the tank has four sides and a bottom, but not a top, its surface area is

$A = 2\cdot 78.4\cdot 19.6 + 2\cdot 39.2\cdot 19.6 + 78.4\cdot 39.2$

$A = 2\cdot 78.4\cdot 19.6 + 2\cdot 39.2\cdot 19.6 + 78.4\cdot 39.2 \approx 7,683$

The surface area of the tank is about 7,683 square feet.

Compare your answer with the correct one above

Question

A rectangular prism has a volume of . If the length of the prism is and its width is , what is its height?

Answer

The volume of a rectangular prism is equal to its length times its width times its height. We are given the volume, the length, and the width, so using the following formula we can solve for the height of the rectangular prism:

$H=\frac{105}{35}=3$

Compare your answer with the correct one above

Question

Jenny wants to make a cube out of sheet metal. What is the length of one side of the cube?

I) The cube will require square inches of material.

II) The cube will hold cubic inches.

Answer

The length of an edge of a cube can be used to find either volume or surface area, and vice versa.

I) Gives us the surface area thus, we are able to calculate the length of an edge using the formula,

$SA=6\cdot s^2$

$294=6s^2 \rightarrow 49=s^2 \rightarrow 7=s$ .

II) Gives us the volume thus, we are able to calculate the length of an edge using the formula,

$343=s^3 \rightarrow 7=s$

Either can be used to find the side length.

Compare your answer with the correct one above

Question

A rectangular prism has a volume of , a length of , and a height of . What is the width of the prism?

Answer

Using the formula for the volume of a rectangular prism, we can plug in the given values and solve for the width of the prism:

$W=\frac{70}{14}=5$

Compare your answer with the correct one above

Question

A rectangular prism has a surface area of , a width of , and a height of . What is the length of the prism?

Answer

We are given the surface area and the length of two sides, so in order to calculate the length of the third side we need the formula for the surface area of a prism in terms of each side length:

Using the formula, we can simply plug in the given values and solve for the length of the rectangular prism:

Compare your answer with the correct one above

Question

A new fish tank at a theme park must hold 450,000 gallons of sea water. Its dimensions must be such that it is twice as long as it is wide, and half as high as it is wide. If one gallon of water occupies 0.1337 cubic feet, then give the surface area of the proposed tank to the nearest square foot.

You may assume that the tank has all four sides and a bottom, but is open at the top.

Answer

450,000 gallons of water occupy $\small \small 0.1337 \cdot 450,000 \approx 60,165$ cubic feet.

Let $\small h$ be the height of the tank. Then the width of the tank is , and its length is . Multiply the dimensions to get the volume:

$V = LWH = H \cdot 2H\cdot 4H = 8H^{3} = 60,165$

$H^{3} = 60,165 \div 8 \approx 7,521$

$H = \sqrt[3]{7,521} \approx 19.6$

$W = 2H = 2 \cdot19.6 = 39.2$

$L = 2W = 2\cdot 39.2 = 78.4$

Since the tank has four sides and a bottom, but not a top, its surface area is

$A = 2\cdot 78.4\cdot 19.6 + 2\cdot 39.2\cdot 19.6 + 78.4\cdot 39.2$

$A = 2\cdot 78.4\cdot 19.6 + 2\cdot 39.2\cdot 19.6 + 78.4\cdot 39.2 \approx 7,683$

The surface area of the tank is about 7,683 square feet.

Compare your answer with the correct one above

Question

A rectangular prism has a volume of . If the length of the prism is and its width is , what is its height?

Answer

The volume of a rectangular prism is equal to its length times its width times its height. We are given the volume, the length, and the width, so using the following formula we can solve for the height of the rectangular prism:

$H=\frac{105}{35}=3$

Compare your answer with the correct one above

Question

Jenny wants to make a cube out of sheet metal. What is the length of one side of the cube?

I) The cube will require square inches of material.

II) The cube will hold cubic inches.

Answer

The length of an edge of a cube can be used to find either volume or surface area, and vice versa.

I) Gives us the surface area thus, we are able to calculate the length of an edge using the formula,

$SA=6\cdot s^2$

$294=6s^2 \rightarrow 49=s^2 \rightarrow 7=s$ .

II) Gives us the volume thus, we are able to calculate the length of an edge using the formula,

$343=s^3 \rightarrow 7=s$

Either can be used to find the side length.

Compare your answer with the correct one above

Question

A rectangular prism has a volume of , a length of , and a height of . What is the width of the prism?

Answer

Using the formula for the volume of a rectangular prism, we can plug in the given values and solve for the width of the prism:

$W=\frac{70}{14}=5$

Compare your answer with the correct one above

Question

A rectangular prism has a surface area of , a width of , and a height of . What is the length of the prism?

Answer

We are given the surface area and the length of two sides, so in order to calculate the length of the third side we need the formula for the surface area of a prism in terms of each side length:

Using the formula, we can simply plug in the given values and solve for the length of the rectangular prism:

Compare your answer with the correct one above

Question

A new fish tank at a theme park must hold 450,000 gallons of sea water. Its dimensions must be such that it is twice as long as it is wide, and half as high as it is wide. If one gallon of water occupies 0.1337 cubic feet, then give the surface area of the proposed tank to the nearest square foot.

You may assume that the tank has all four sides and a bottom, but is open at the top.

Answer

450,000 gallons of water occupy $\small \small 0.1337 \cdot 450,000 \approx 60,165$ cubic feet.

Let $\small h$ be the height of the tank. Then the width of the tank is , and its length is . Multiply the dimensions to get the volume:

$V = LWH = H \cdot 2H\cdot 4H = 8H^{3} = 60,165$

$H^{3} = 60,165 \div 8 \approx 7,521$

$H = \sqrt[3]{7,521} \approx 19.6$

$W = 2H = 2 \cdot19.6 = 39.2$

$L = 2W = 2\cdot 39.2 = 78.4$

Since the tank has four sides and a bottom, but not a top, its surface area is

$A = 2\cdot 78.4\cdot 19.6 + 2\cdot 39.2\cdot 19.6 + 78.4\cdot 39.2$

$A = 2\cdot 78.4\cdot 19.6 + 2\cdot 39.2\cdot 19.6 + 78.4\cdot 39.2 \approx 7,683$

The surface area of the tank is about 7,683 square feet.

Compare your answer with the correct one above

Question

A rectangular prism has a volume of . If the length of the prism is and its width is , what is its height?

Answer

The volume of a rectangular prism is equal to its length times its width times its height. We are given the volume, the length, and the width, so using the following formula we can solve for the height of the rectangular prism:

$H=\frac{105}{35}=3$

Compare your answer with the correct one above

Question

Jenny wants to make a cube out of sheet metal. What is the length of one side of the cube?

I) The cube will require square inches of material.

II) The cube will hold cubic inches.

Answer

The length of an edge of a cube can be used to find either volume or surface area, and vice versa.

I) Gives us the surface area thus, we are able to calculate the length of an edge using the formula,

$SA=6\cdot s^2$

$294=6s^2 \rightarrow 49=s^2 \rightarrow 7=s$ .

II) Gives us the volume thus, we are able to calculate the length of an edge using the formula,

$343=s^3 \rightarrow 7=s$

Either can be used to find the side length.

Compare your answer with the correct one above

Question

A rectangular prism has a volume of , a length of , and a height of . What is the width of the prism?

Answer

Using the formula for the volume of a rectangular prism, we can plug in the given values and solve for the width of the prism:

$W=\frac{70}{14}=5$

Compare your answer with the correct one above

Question

A rectangular prism has a surface area of , a width of , and a height of . What is the length of the prism?

Answer

We are given the surface area and the length of two sides, so in order to calculate the length of the third side we need the formula for the surface area of a prism in terms of each side length:

Using the formula, we can simply plug in the given values and solve for the length of the rectangular prism:

Compare your answer with the correct one above

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