Question

Rachel has a box in the shape of a prism with a square base. The capacity of the box is 150 cubic inches. The height of the box (y) is times the base length of the box (x). Find the approximate height and the length of the box.

A. x = 4 and y = 6
B. x = 5 and y = 7.5
C. x = 4.2 and y = 6.3
D. x = 4.6 and y = 6.9

Answer 1

Explanation:

What do we know about that prism?

It's a rectangular prism with a square base.

Height: y (from question)

base length: x (from question)

base width: x (from question, since it's a square base).

Total volume: 150 cu inches

The question lacks a relationship between x and y the "is __ times", but we can see from the answer choices that they all show a constant relationship:

y = 1.5 x

The volume of a prism is obtained by multiplying the lengths of its 3 dimensions: V = length * width * height. In our case, we then have

150 = x * x * y

then we replace y by its x-expressed equivalent:

150 = x * x * (1.5x) = 1.5x³

then we isolate x³ by dividing each side by 1.5

x³ = 100, we do the cubic root on each side

x = 4.64

So, answer is D. x = 4.6 and y = 6.9

If you you 4.64 * 4.64 * 6.96 = you get 149.8, which is very close to 150.