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# A solid composed of a cylinder with hemispherical ends on both sides. The radius and height of the cylinder are 20 cm and 30 cm respectively. Find the total surface area of the solid. Take $\pi =3\cdot 14$.

Last updated date: 12th Jul 2024
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Hint: First assume radius of cylinder = radius of hemisphere = $r$. Let height of the cylinder $=h$. Then we should use the formulas, Lateral surface area (L.S.A.) of cylinder $=2\pi rh$, Lateral surface area (L.S.A.) of hemisphere $=2\pi {{r}^{2}}$, to calculate the area we need in the question.

Let the height of the cylinder is $h$. Since the radii of the hemisphere and cylinder are equal, we assume their radius as $r$.
We have been given that $r=20\text{ cm}$ and $h=30\text{ cm}$.
Required T.S.A. of solid $=$ L.S.A. of cylinder $+$ L.S.A. of hemisphere.
Required T.S.A. of solid $=2\pi rh+2\pi {{r}^{2}}...................................(1)$
Substituting the given values of $r$ and $h$ in equation $(1)$, we get;
\begin{align} & \text{Required T}\text{.S}\text{.A}\text{. of solid}=2\times 3.14\times 20\times 30+4\times 3.14\times {{20}^{2}} \\ & \text{ }=3768+5024 \\ & \text{ }=8792\text{ c}{{\text{m}}^{2}} \\ \end{align}