Question
Volume and surface area of a solid hemisphere are numerically equal.
What is the diameter of hemisphere?
What is the diameter of hemisphere?
✓
Answer
We know that volume of a solid hemisphere is given by
$
V=\frac{2}{3} \pi r^3
$
Also, surface area of a solid hemisphere is given by
$
S=3 \pi r^2
$
Where, $r$ is the radius of the solid hemisphere According to the question,
Volume and surface area of a solid hemisphere are numerically equal
$
\begin{aligned}
\frac{2}{3} \pi r^3 & =3 \pi r^2 \\
\Rightarrow 2 r & =9
\end{aligned}
$
We know that $2 r=$ diameter
$\Rightarrow$ diameter $=9$ units
Hence, the diameter of the solid hemisphere is 9 units.
$
V=\frac{2}{3} \pi r^3
$
Also, surface area of a solid hemisphere is given by
$
S=3 \pi r^2
$
Where, $r$ is the radius of the solid hemisphere According to the question,
Volume and surface area of a solid hemisphere are numerically equal
$
\begin{aligned}
\frac{2}{3} \pi r^3 & =3 \pi r^2 \\
\Rightarrow 2 r & =9
\end{aligned}
$
We know that $2 r=$ diameter
$\Rightarrow$ diameter $=9$ units
Hence, the diameter of the solid hemisphere is 9 units.
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