Question

Cube A and Cube B are similar solids. the volume of cube A is 27 cubic inches , and the volume of cube B is 125 cubic inches. how many times larger is the base area of cube b than the base area of cube A?

Answer 1

A.
`(25)/(9)`

Explanation:

We have been given that Cube A and Cube B are similar solids. The volume of cube A is 27 cubic inches, and the volume of cube B is 125 cubic inches. We are asked to find the the number of times the base area of cube b is larger than the base area of cube A.

We know that volume of cube with each side of
`x` units is equal to
`x^3`.

First of all, we will find the each side of cube A and B as:

`A^3=27`

`\sqrt[3]{A^3} =\sqrt[3]{27}`

`A=3`

`B^3=125`

`\sqrt[3]{B^3} =\sqrt[3]{125}`

`B=5`

Now, we will find base area of both cubes as:

`\frac{\text{Base area of cube B}}{\text{Base area of cube A}}=(B^2)/(A^2)`

`\frac{\text{Base area of cube B}}{\text{Base area of cube A}}=(5^2)/(3^2)`

`\frac{\text{Base area of cube B}}{\text{Base area of cube A}}=(25)/(9)`

Therefore, the base area of cube B is
`(25)/(9)` times larger than the base area of cube A.