Question

The radius of a softball is 3.75 cm, and the radius of a table tennis ball is 2 cm. The volume of the softball is how many times greater than the volume of the table tennis ball? show your work using radius. use 3.14 for pi. round to the nearest tenth

Answer 1

The volume of the softball is 6.6 times the volume of the tennis ball

Explanation:

we know that

The volume of a sphere is equal to

`V=(4)/(3)\pi r^(3)`

step 1

Find the volume of the softball

we have

`r=3.75\ cm`

substitute

`V=(4)/(3)(3.14)(3.75)^(3)=220.8\ cm^(3)`

step 2

Find the volume of the tennis ball

we have

`r=2\ cm`

substitute

`V=(4)/(3)(3.14)(2)^(3)=33.5\ cm^(3)`

step 3

Divide the volume of the softball by the volume of the tennis ball

`220.8\ cm^(3)/33.5\ cm^(3)=6.6`

therefore

The volume of the softball is 6.6 times the volume of the tennis ball

Alternative Method

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

The scale factor is equal to the ratio of its radius

`(3.75)/(2)=1.875`

therefore

The scale factor elevated to the cube is

`1.875^(3)=6.6`

therefore

The volume of the softball is 6.6 times the volume of the tennis ball