How to find the volume of a prism

Help Questions

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

Questions 1 - 4

1

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.

$8 \frac{8}{9 } \textrm{ yd}^{3}$

$7 \frac{2}{9 } \textrm{ yd}^{3}$

$10 \textrm{ yd}^{3}$

$80 \textrm{ yd}^{3}$

$90\textrm{ yd}^{3}$

Explanation

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

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

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

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

2

Box

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

$15x^{2}$

$4x^{2} + 30 x$

Explanation

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:

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

3

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.

Explanation

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:

4

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

(B) is greater

(A) is greater

(A) and (B) are equal

It is impossible to determine which is greater from the information given

Explanation

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

Return to subject