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.

Answer

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

Compare your answer with the correct one above

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

Answer

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

Compare your answer with the correct one above

Question

Box

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

Answer

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

Box

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

.

Compare your answer with the correct one above

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.

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:

Compare your answer with the correct one above

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.

Answer

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

Compare your answer with the correct one above

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

Answer

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

Compare your answer with the correct one above

Question

Box

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

Answer

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

Box

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

.

Compare your answer with the correct one above

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.

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:

Compare your answer with the correct one above

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.

Answer

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

Compare your answer with the correct one above

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

Answer

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

Compare your answer with the correct one above

Question

Box

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

Answer

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

Box

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

.

Compare your answer with the correct one above

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.

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:

Compare your answer with the correct one above

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.

Answer

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

Compare your answer with the correct one above

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

Answer

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

Compare your answer with the correct one above

Question

Box

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

Answer

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

Box

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

.

Compare your answer with the correct one above

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.

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:

Compare your answer with the correct one above

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