Question

A prism with a base area of 5 ft² and a height of 10 ft is dilated by a factor of 6/5 .

What is the volume of the dilated prism?

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

Answer 1

First we need to find the volume of the prism without the dilated factor:

The volume would be:
Volume of the prism(without dilated) = (area of the base) * (height)
Since,
Area of base = 5
`ft^(2)`
Height of the prism = 10f

Volume(without dilated) = 5*10 = 50
`ft^(3)`

Now let us apply the dilated factor! For that you need to multiply for factor with the volume of the prism without dilation.

Volume of the dilated prism =
`d^(3)` * (Volume of the prism without dilation)

Where d = dilated factor. Therefore,


`v = ((6)/(5) )^(3) * 50`


v = 86.4
`ft^(3)`

So the correct answer: 86.4
`ft^(3)`