Question

A prism with a base area of 8 cm² and a height of 6 cm is dilated by a factor of 54 . What is the volume of the dilated prism? Enter your answer, as a decimal, in the box

Answer 1

Question:

A prism with a base area of 8 cm² 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:

The volume of the dilated prism is
`93.75 \ {cm}^(3)`

Step-by-step explanation:

A prism with a base area of 8 cm² and a height of 6 cm

The volume of the prism can be determined by the formula,
`V=Bh`

Volume of the prism is given by

`V=Bh`

`V=(8)(6)`

`V=46\ cm^3`

Thus, the volume of the prism is
`46 \ {cm}^(3)`

It is also given that the volume of the dilated prism is dilated by a factor of
`(5)/(4)`

Hence, the new volume is given by

`Volume = 48((5)/(4) )^3`

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

`=48(1.953125)`

`=93.75 \ {cm}^(3)`

Thus, the volume of the dilated prism is
`93.75 \ {cm}^(3)`