Question

A cone has a radius of 15 cm and a volume of 540 cm^3. what is the volume of a similar cone with a radius of 10 cm?

Answer 1

160 cubic centimeters

Explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

Let

z ---> the scale factor

`z=(10)/(15)` ----> the ratio of corresponding radii

simplify

`z=(2)/(3)`

step 2

Find the volume of the smaller cone

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 ---> the scale factor

x ----> the volume of the smaller cone

y ---> the volume of the larger cone

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

we have

`z=(2)/(3)`

`y=540\ cm^3`

substitute

`((2)/(3))^(3)=(x)/(540)`

`x=540((2)/(3))^(3)`

`x=160\ cm^3`