Question

The ratio of the radio of sphere A and sphere B is Ra\Rb =2/5. The volume of sphere b is 64 pied cu ft. What is the volume of sphere A

Answer 1

The volume of a sphere with radius
`r` is
`V=\frac43\pi r^3`. Sphere B has a volume of
`64\pi`, so

`V_B=\frac43\pi{r_B}^3\implies r_B=\sqrt[3]{(64\pi)/(\frac43\pi)}=\sqrt[3]{48}`

Now,

`(r_A)/(r_B)=\frac25\implies r_A=\frac{2r_B}5`

so sphere A has volume

`V_A=\frac43\pi\left(\frac{2r_B}5\right)^3=(512)/(125)\pi`