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 $93.75 \ {cm}^{3}$

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 $\frac{5}{4}$

Hence, the new volume is given by

$Volume = 48(\frac{5}{4} )^3$

             $=48(\frac{125}{64} )$

             $=48(1.953125)$

             $=93.75 \ {cm}^{3}$

Thus, the volume of the dilated prism is $93.75 \ {cm}^{3}$