Question

A prism with a base area of 8 cm^2 and a height of 6 cm is dilated by a factor of 5/4.

What is the volume of the dilated prism?
Enter your answer as a decimal in the box.

Answer 1

The dilated volume will be 93.75 cm³

Explanation:

Let us first find the original volume

Original volume = 8 * 6 = 48 cm³

Now

The original volume will increase by a cube of the scale factor because it is a prism

So

48 * (5/4)³

= [48 * 125] / 64

= [48/64] * 125

= (3/4) * 125

= 93.75 cm³

Answer 2

`93.75cm^3`

Explanation:

First, calculate the volume of the original prism using;

`v=base\:area* height`

`\Rightarrow v=8* 6`

`\Rightarrow v=48cm^3`

Next, find the volume of the dilated prism by multiplying the original prism by;

`k^3=(125)/(64)`

Volume of dilated prism;

`V=(125)/(64)* 48`

`V=93.75.0cm^3`