1.

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

Answer»

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...


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