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.

Answer 1

Answer:

$93.75cm^3$

Step-by-step explanation:

First, calculate the volume of the original prism using;

$v=base\:area\times height$

$\Rightarrow v=8\times 6$

$\Rightarrow v=48cm^3$

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

$k^3=\frac{125}{64}$

Volume of dilated prism;

$V=\frac{125}{64}\times 48$

$V=93.75.0cm^3$

Answer 2

Answer:

The dilated volume will be 93.75 cm³

Step-by-step 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