Question

surface areas of sphere and cube are equal.find the ratio of their volumes

Answer 1

radius of a sphere =r and side of a cube=a.
given that surface areas of sphere and cube are equal. surface area of sphere= surface area of cube
=>
$4\pi {r}^{2} = 6 {a}^{2}$
=>
${r}^{2} \div {a}^{2} = 6 \div 4\pi$
on applying square root to it, we get
=> r/a=0.6911
=> ratio of their volumes =
$\frac{4\pi {r}^{3} }{ 3{a}^{3} }$
=> ratio of their volumes =
$\frac{4}{3} \ ( {0.6911})^{3}$
=> ratio of their volumes = 0.44011081~0.44 approximately...