Question

4.) 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?

Answer 1

93.75 cm^3

Step-by-step explanation:

Given the following;

Base area of the prism = 8 cm^2

Height of the prism = 6cm

Scale factor = 5/4

Let's go ahead and determine the volume of the original prism before the dilation;

`\text{Volume of original prism = Base area x Height }=8\cdot6=48cm^3`

So the volume of the original prism before dilation is 48cm^3

Let's go ahead and determine the volume of the dilated prism as seen below;

`\begin{gathered} \text{Volume of dilated prism }=\text{Volume of original prism x (Scale factor)\textasciicircum{}3} \\ =48\cdot((5)/(4))^3 \\ =48\cdot(125)/(64) \\ =93.75cm^3 \end{gathered}`

So the volume of the dilated prism is 93.75 cm^3