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

Answer:

$40\ m^{3}$

Step-by-step 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

$z^{3}=\frac{x}{y}$

In this problem we have

$z=1/5$

$y=5,000\ m^{3}$

substitute and solve for x

$(1/5)^{3}=\frac{x}{5,000}$

$(1/125)=\frac{x}{5,000}$

$x=5,000/125=40\ m^{3}$