Question

A prism with a base area of 5 ft² and a height of 10 ft is dilated by a factor of 65 . What is the volume of the dilated prism? Enter your answer, as a decimal, in the box. ft³

Answer 1

The answer is 86.4

Answer 2

The volume of the dilated prism is
`86.4ft^3`.

Explanation:

The original prism has base area
`5ft^2` and a height of
`10ft`.

The volume of the original prism is
`v=5* 10=50ft^3`.

The prism is dilated by a scale factor of
`k=(6)/(5)`.

To find the volume of the dilated prism, we multiply the volume of the original prism by
`k^3=(216)/(125)`.

`V=(216)/(125) * 50ft^3`

`\Rightarrow V=86.4ft^3`