Question

A prism with a base area of 3 m² and a height of 4 m is dilated by a factor of 32 .



What is the volume of the dilated prism?

Enter your answer, as a decimal, in the box.


The Answer is 40.5, because i'm taking the test right now.

Answer 1

The answer to this is 40.5

Answer 2

ANSWER

$40.5 {m}^{3}$

EXPLANATION


The given prism has a base area of 3m² and a height of 4m.


The volume of this prism is,

$= base \: area \times \: height$


$= 3 \times 4 {m}^{3}$


$=12{m}^{3}$


If this prism prism is dilated by a scale factor of

$k = \frac{3}{2}$

The scale factor for the volume becomes,

${k}^{3} = \frac{27}{8}$


We multiply the volume of the given prism by the scale factor of the volume to obtain the volume of the dilated prism to be,

$= 12 \times \frac{27}{8} {m}^{3}$



$=40.5{m}^{3}$