How to find the volume of a prism - ISEE Upper Level: Quantitative Reasoning

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Question

A large crate in the shape of a rectangular prism has dimensions 5 feet by 4 feet by 12 feet. Give its volume in cubic yards.

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Answer

Divide each dimension by 3 to convert feet to yards, then multiply the three dimensions together:

$V = \frac{5}{3} \cdot \frac{4}{3} \cdot \frac{12}{3}$

$V = \frac{5}{3} \cdot \frac{4}{3} \cdot \frac{4}{1}$

$V = \frac{80}{9 } = 8 \frac{8}{9 } \textrm{ yd}^{3}$

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Question

Which is the greater quantity?

(A) The volume of a rectangular solid ten inches by twenty inches by fifteen inches

(B) The volume of a cube with sidelength sixteen inches

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Answer

The volume of a rectangular solid ten inches by twenty inches by fifteen inches is

$V = 10 \cdot 20 \cdot15 = 3,000$ cubic inches.

The volume of a cube with sidelength 13 inches is

$V = 16^{3} = 16 \cdot 16 \cdot 16 = 4,096$ cubic inches.

This makes (B) greater

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Question

The above diagram shows a rectangular solid. The shaded side is a square. In terms of , give the volume of the box.

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Answer

A square has four sides of equal length, as seen in the diagram below.

The volume of the solid is equal to the product of its length, width, and height, as follows:

$V = 15 \cdot 15 \cdot x =225 x$ .

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Question

A rectangular prism has a width of 3 inches, a length of 6 inches, and a height triple its length. Find the volume of the prism.

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Answer

A rectangular prism has a width of 3 inches, a length of 6 inches, and a height triple its length. Find the volume of the prism.

Find the volume of a rectangular prism via the following:

Where l, w, and h are the length width and height, respectively.

We know our length and width, and we are told that our height is triple the length, so...

Now that we have all our measurements, plug them in and solve:

← Didn't Know|Knew It →

Question

A large crate in the shape of a rectangular prism has dimensions 5 feet by 4 feet by 12 feet. Give its volume in cubic yards.

Tap to reveal answer

Answer

Divide each dimension by 3 to convert feet to yards, then multiply the three dimensions together:

$V = \frac{5}{3} \cdot \frac{4}{3} \cdot \frac{12}{3}$

$V = \frac{5}{3} \cdot \frac{4}{3} \cdot \frac{4}{1}$

$V = \frac{80}{9 } = 8 \frac{8}{9 } \textrm{ yd}^{3}$

← Didn't Know|Knew It →

Question

Which is the greater quantity?

(A) The volume of a rectangular solid ten inches by twenty inches by fifteen inches

(B) The volume of a cube with sidelength sixteen inches

Tap to reveal answer

Answer

The volume of a rectangular solid ten inches by twenty inches by fifteen inches is

$V = 10 \cdot 20 \cdot15 = 3,000$ cubic inches.

The volume of a cube with sidelength 13 inches is

$V = 16^{3} = 16 \cdot 16 \cdot 16 = 4,096$ cubic inches.

This makes (B) greater

← Didn't Know|Knew It →

Question

The above diagram shows a rectangular solid. The shaded side is a square. In terms of , give the volume of the box.

Tap to reveal answer

Answer

A square has four sides of equal length, as seen in the diagram below.

The volume of the solid is equal to the product of its length, width, and height, as follows:

$V = 15 \cdot 15 \cdot x =225 x$ .

← Didn't Know|Knew It →

Question

A rectangular prism has a width of 3 inches, a length of 6 inches, and a height triple its length. Find the volume of the prism.

Tap to reveal answer

Answer

A rectangular prism has a width of 3 inches, a length of 6 inches, and a height triple its length. Find the volume of the prism.

Find the volume of a rectangular prism via the following:

Where l, w, and h are the length width and height, respectively.

We know our length and width, and we are told that our height is triple the length, so...

Now that we have all our measurements, plug them in and solve:

← Didn't Know|Knew It →

Question

A large crate in the shape of a rectangular prism has dimensions 5 feet by 4 feet by 12 feet. Give its volume in cubic yards.

Tap to reveal answer

Answer

Divide each dimension by 3 to convert feet to yards, then multiply the three dimensions together:

$V = \frac{5}{3} \cdot \frac{4}{3} \cdot \frac{12}{3}$

$V = \frac{5}{3} \cdot \frac{4}{3} \cdot \frac{4}{1}$

$V = \frac{80}{9 } = 8 \frac{8}{9 } \textrm{ yd}^{3}$

← Didn't Know|Knew It →

Question

Which is the greater quantity?

(A) The volume of a rectangular solid ten inches by twenty inches by fifteen inches

(B) The volume of a cube with sidelength sixteen inches

Tap to reveal answer

Answer

The volume of a rectangular solid ten inches by twenty inches by fifteen inches is

$V = 10 \cdot 20 \cdot15 = 3,000$ cubic inches.

The volume of a cube with sidelength 13 inches is

$V = 16^{3} = 16 \cdot 16 \cdot 16 = 4,096$ cubic inches.

This makes (B) greater

← Didn't Know|Knew It →

Question

The above diagram shows a rectangular solid. The shaded side is a square. In terms of , give the volume of the box.

Tap to reveal answer

Answer

A square has four sides of equal length, as seen in the diagram below.

The volume of the solid is equal to the product of its length, width, and height, as follows:

$V = 15 \cdot 15 \cdot x =225 x$ .

← Didn't Know|Knew It →

Question

A rectangular prism has a width of 3 inches, a length of 6 inches, and a height triple its length. Find the volume of the prism.

Tap to reveal answer

Answer

A rectangular prism has a width of 3 inches, a length of 6 inches, and a height triple its length. Find the volume of the prism.

Find the volume of a rectangular prism via the following:

Where l, w, and h are the length width and height, respectively.

We know our length and width, and we are told that our height is triple the length, so...

Now that we have all our measurements, plug them in and solve:

← Didn't Know|Knew It →

Question

A large crate in the shape of a rectangular prism has dimensions 5 feet by 4 feet by 12 feet. Give its volume in cubic yards.

Tap to reveal answer

Answer

Divide each dimension by 3 to convert feet to yards, then multiply the three dimensions together:

$V = \frac{5}{3} \cdot \frac{4}{3} \cdot \frac{12}{3}$

$V = \frac{5}{3} \cdot \frac{4}{3} \cdot \frac{4}{1}$

$V = \frac{80}{9 } = 8 \frac{8}{9 } \textrm{ yd}^{3}$

← Didn't Know|Knew It →

Question

Which is the greater quantity?

(A) The volume of a rectangular solid ten inches by twenty inches by fifteen inches

(B) The volume of a cube with sidelength sixteen inches

Tap to reveal answer

Answer

The volume of a rectangular solid ten inches by twenty inches by fifteen inches is

$V = 10 \cdot 20 \cdot15 = 3,000$ cubic inches.

The volume of a cube with sidelength 13 inches is

$V = 16^{3} = 16 \cdot 16 \cdot 16 = 4,096$ cubic inches.

This makes (B) greater

← Didn't Know|Knew It →

Question

The above diagram shows a rectangular solid. The shaded side is a square. In terms of , give the volume of the box.

Tap to reveal answer

Answer

A square has four sides of equal length, as seen in the diagram below.

The volume of the solid is equal to the product of its length, width, and height, as follows:

$V = 15 \cdot 15 \cdot x =225 x$ .

← Didn't Know|Knew It →

Question

A rectangular prism has a width of 3 inches, a length of 6 inches, and a height triple its length. Find the volume of the prism.

Tap to reveal answer

Answer

A rectangular prism has a width of 3 inches, a length of 6 inches, and a height triple its length. Find the volume of the prism.

Find the volume of a rectangular prism via the following:

Where l, w, and h are the length width and height, respectively.

We know our length and width, and we are told that our height is triple the length, so...

Now that we have all our measurements, plug them in and solve:

← Didn't Know|Knew It →

Knew It

How to find the volume of a prism - ISEE Upper Level: Quantitative Reasoning

A large crate in the shape of a rectangular prism has dimensions 5 feet by 4 feet by 12 feet. Give its volume in cubic yards.

Divide each dimension by 3 to convert feet to yards, then multiply the three dimensions together:

Which is the greater quantity? (A) The volume of a rectangular solid ten inches by twenty inches by fifteen inches (B) The volume of a cube with sidelength sixteen inches

The volume of a rectangular solid ten inches by twenty inches by fifteen inches is cubic inches. The volume of a cube with sidelength 13 inches is cubic inches. This makes (B) greater

The above diagram shows a rectangular solid. The shaded side is a square. In terms of , give the volume of the box.

A square has four sides of equal length, as seen in the diagram below. The volume of the solid is equal to the product of its length, width, and height, as follows: .

A rectangular prism has a width of 3 inches, a length of 6 inches, and a height triple its length. Find the volume of the prism.

A large crate in the shape of a rectangular prism has dimensions 5 feet by 4 feet by 12 feet. Give its volume in cubic yards.

Divide each dimension by 3 to convert feet to yards, then multiply the three dimensions together:

Which is the greater quantity? (A) The volume of a rectangular solid ten inches by twenty inches by fifteen inches (B) The volume of a cube with sidelength sixteen inches

The volume of a rectangular solid ten inches by twenty inches by fifteen inches is cubic inches. The volume of a cube with sidelength 13 inches is cubic inches. This makes (B) greater

The above diagram shows a rectangular solid. The shaded side is a square. In terms of , give the volume of the box.

A square has four sides of equal length, as seen in the diagram below. The volume of the solid is equal to the product of its length, width, and height, as follows: .

A rectangular prism has a width of 3 inches, a length of 6 inches, and a height triple its length. Find the volume of the prism.

A large crate in the shape of a rectangular prism has dimensions 5 feet by 4 feet by 12 feet. Give its volume in cubic yards.

Divide each dimension by 3 to convert feet to yards, then multiply the three dimensions together:

Which is the greater quantity? (A) The volume of a rectangular solid ten inches by twenty inches by fifteen inches (B) The volume of a cube with sidelength sixteen inches

The volume of a rectangular solid ten inches by twenty inches by fifteen inches is cubic inches. The volume of a cube with sidelength 13 inches is cubic inches. This makes (B) greater

The above diagram shows a rectangular solid. The shaded side is a square. In terms of , give the volume of the box.

A square has four sides of equal length, as seen in the diagram below. The volume of the solid is equal to the product of its length, width, and height, as follows: .

A rectangular prism has a width of 3 inches, a length of 6 inches, and a height triple its length. Find the volume of the prism.

A large crate in the shape of a rectangular prism has dimensions 5 feet by 4 feet by 12 feet. Give its volume in cubic yards.

Divide each dimension by 3 to convert feet to yards, then multiply the three dimensions together:

Which is the greater quantity? (A) The volume of a rectangular solid ten inches by twenty inches by fifteen inches (B) The volume of a cube with sidelength sixteen inches

The volume of a rectangular solid ten inches by twenty inches by fifteen inches is cubic inches. The volume of a cube with sidelength 13 inches is cubic inches. This makes (B) greater

The above diagram shows a rectangular solid. The shaded side is a square. In terms of , give the volume of the box.

A square has four sides of equal length, as seen in the diagram below. The volume of the solid is equal to the product of its length, width, and height, as follows: .

A rectangular prism has a width of 3 inches, a length of 6 inches, and a height triple its length. Find the volume of the prism.

Divide each dimension by 3 to convert feet to yards, then multiply the three dimensions together:

$V = \frac{5}{3} \cdot \frac{4}{3} \cdot \frac{12}{3}$

$V = \frac{5}{3} \cdot \frac{4}{3} \cdot \frac{4}{1}$

$V = \frac{80}{9 } = 8 \frac{8}{9 } \textrm{ yd}^{3}$

Which is the greater quantity?

(A) The volume of a rectangular solid ten inches by twenty inches by fifteen inches

(B) The volume of a cube with sidelength sixteen inches

The volume of a rectangular solid ten inches by twenty inches by fifteen inches is

$V = 10 \cdot 20 \cdot15 = 3,000$ cubic inches.

The volume of a cube with sidelength 13 inches is

$V = 16^{3} = 16 \cdot 16 \cdot 16 = 4,096$ cubic inches.

This makes (B) greater

A square has four sides of equal length, as seen in the diagram below.

The volume of the solid is equal to the product of its length, width, and height, as follows:

$V = 15 \cdot 15 \cdot x =225 x$ .

Divide each dimension by 3 to convert feet to yards, then multiply the three dimensions together:

$V = \frac{5}{3} \cdot \frac{4}{3} \cdot \frac{12}{3}$

$V = \frac{5}{3} \cdot \frac{4}{3} \cdot \frac{4}{1}$

$V = \frac{80}{9 } = 8 \frac{8}{9 } \textrm{ yd}^{3}$

Which is the greater quantity?

(A) The volume of a rectangular solid ten inches by twenty inches by fifteen inches

(B) The volume of a cube with sidelength sixteen inches

The volume of a rectangular solid ten inches by twenty inches by fifteen inches is

$V = 10 \cdot 20 \cdot15 = 3,000$ cubic inches.

The volume of a cube with sidelength 13 inches is

$V = 16^{3} = 16 \cdot 16 \cdot 16 = 4,096$ cubic inches.

This makes (B) greater

A square has four sides of equal length, as seen in the diagram below.

The volume of the solid is equal to the product of its length, width, and height, as follows:

$V = 15 \cdot 15 \cdot x =225 x$ .

Divide each dimension by 3 to convert feet to yards, then multiply the three dimensions together:

$V = \frac{5}{3} \cdot \frac{4}{3} \cdot \frac{12}{3}$

$V = \frac{5}{3} \cdot \frac{4}{3} \cdot \frac{4}{1}$

$V = \frac{80}{9 } = 8 \frac{8}{9 } \textrm{ yd}^{3}$

Which is the greater quantity?

(A) The volume of a rectangular solid ten inches by twenty inches by fifteen inches

(B) The volume of a cube with sidelength sixteen inches

The volume of a rectangular solid ten inches by twenty inches by fifteen inches is

$V = 10 \cdot 20 \cdot15 = 3,000$ cubic inches.

The volume of a cube with sidelength 13 inches is

$V = 16^{3} = 16 \cdot 16 \cdot 16 = 4,096$ cubic inches.

This makes (B) greater

A square has four sides of equal length, as seen in the diagram below.

The volume of the solid is equal to the product of its length, width, and height, as follows:

$V = 15 \cdot 15 \cdot x =225 x$ .

Divide each dimension by 3 to convert feet to yards, then multiply the three dimensions together:

$V = \frac{5}{3} \cdot \frac{4}{3} \cdot \frac{12}{3}$

$V = \frac{5}{3} \cdot \frac{4}{3} \cdot \frac{4}{1}$

$V = \frac{80}{9 } = 8 \frac{8}{9 } \textrm{ yd}^{3}$

Which is the greater quantity?

(A) The volume of a rectangular solid ten inches by twenty inches by fifteen inches

(B) The volume of a cube with sidelength sixteen inches

The volume of a rectangular solid ten inches by twenty inches by fifteen inches is

$V = 10 \cdot 20 \cdot15 = 3,000$ cubic inches.

The volume of a cube with sidelength 13 inches is

$V = 16^{3} = 16 \cdot 16 \cdot 16 = 4,096$ cubic inches.

This makes (B) greater

A square has four sides of equal length, as seen in the diagram below.

The volume of the solid is equal to the product of its length, width, and height, as follows:

$V = 15 \cdot 15 \cdot x =225 x$ .