Question

A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 104 cm and the radius of each hemispherical end is 7 cm, find the surface area of the solid.

Answer 1

Radius of the hemispherical end = 7 cm
Height of the hemispherical end = 7 cm
Height of the cylindrical part$=\left(104-2\times 7\right)\text{cm}=90\text{cm}$
Surface area of the solid = 2(curved surface area of the hemisphere) + (curved surface area of the cylinder)
$=\left[2\left(2\mathrm{\pi }{r}^2\right)+2\mathrm{\pi }rh\right]$
$$\begin{gathered} =2\mathrm{\pi }r\left(2r+h\right) \\ =2\times \frac{22}{7}\times 7\times \left[\left(2\times 7\right)+90\right]{\text{cm}}^2 \\ =\left(44\times 104\right){\text{cm}}^2 \\ =4576{\text{cm}}^2 \end{gathered}$$