Question

A cone with volume 5000 m³ is dilated by a scale factor of 15. What is the volume of the resulting cone? Enter your answer in the box. m³

Answer 1

The answer is 40, I just took the test.

Answer 2

`40\ m^(3)`

Explanation:

we know that

If two figures are similar then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> scale factor

x-----> the volume of the dilated cone

y-----> the volume of the original cone

`z^(3)=(x)/(y)`

In this problem we have

`z=1/5`

`y=5,000\ m^(3)`

substitute and solve for x

`(1/5)^(3)=(x)/(5,000)`

`(1/125)=(x)/(5,000)`

`x=5,000/125=40\ m^(3)`