Question

The radius of the large sphere is double the radius of the small sphere.

2 spheres are shown. One sphere has a radius of 3 and the second sphere has a radius of 6.

How many times is the volume of the large sphere than the small sphere?

2
4
6
8

Answer 1

Answer is D. 8

Explanation:

Answer 2

8

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

Remember that all the spheres are similar

Let

z ----> the scale factor

V_1 ---> the volume of the large sphere

V_2 ---> the volume of the small sphere

`z^3=(V_1)/(V_2)`

Find the scale factor

we know that

The radius of the large sphere is double the radius of the small sphere

so

The scale factor is 2

`z=2`

substitute the value oz z

`z^3=(V_1)/(V_2)`

`2^3=(V_1)/(V_2)`

`8=(V_1)/(V_2)`

`V_1=8V_2`

The volume of the large sphere is 8 times the volume of the small sphere