Question

Volume and surface area of a solid hemisphere are numerically equal. what is the diameter of the hemisphere? ​

Answer 1

Given :

Volume and surface area of a solid hemisphere are equal.

To find :

Diameter of hemisphere (d) = ?

Solution :

$we \: know \: that \: \\ volume \: of \: hemisphe \: = surface \: area \: of \: hemisphere \: \\ \frac{2}{3} \pi {r}^{3} \: \: = \: \: 2\pi {r}^{2} \\ \\ \frac{ {r}^{3} }{ {r}^{2} } = \: \frac{2 \times 3}{2} \\ r = 3 \\ \\ \\ now \: \\ diameter \: of \: hemsphere = 2 \times r \\ d = 2 \times r \\ d = 2 \times 3 \\ d = 6 \: units$

Answer :

The diameter of the hemisphere is 6 units.

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