Question

The radius of the large sphere is 3 times longer than the radius of the small sphere. How many times smaller than the volume of the large sphere is the volume of the small sphere?

Answer 1

V=(4p(3r)^3)/3 and v=(4pr^3)/3

V/v=(3r)^3/(r^3)

V/v=9r^3/r^3

V/v=9

So the smaller sphere has a volume that is nine times smaller than the larger.

Answer 2

The volume of the smaller sphere is
`27` times smaller than the volume of the larger sphere

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-------> the scale factor

x-------> the volume of the larger sphere

y-------> the volume of the smaller sphere

so

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

In this problem we have

`z=3`

substitute

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

`27=(x)/(y)`

`y=x/27` -----> The volume of the smaller sphere is
`27` times smaller than the volume of the larger sphere

or

`x=27y` -----> The volume of the larger sphere is
`27` times greater than the volume of the smaller sphere