Question

The radius of the large sphere is double the radius of the small sphere. How many times is the volume of the large sphere than the small sphere? 2 4 6 8

Answer 1

THe ratio of volumes = ratio of the cubes of the radius so it's

2^3 = 8 (answer)

Answer 2

The volume of a sphere is
`\cfrac{4}{3}\ \pi r^3`

So, if the small sphere has radius
`r` and the largest sphere has radius
`2r`, their volumes are

`V_1 = \cfrac{4}{3}\ \pi r^3,\quad V_2 = \cfrac{4}{3}\ \pi (2r)^3 = \cfrac{4}{3}\ \pi 8r^3`

So, their ratio is

`\cfrac{V_2}{V_1} = \cfrac{(4)/(3)\ \pi 8r^3}{(4)/(3)\ \pi r^3} = 8`