Question

A wooden article was made by scooping out a hemisphere from each end of a cylinder, as shown in the figure. If the height of the cylinder is 20 cm and its base diameter is 7 cm, find the total surface area of the article when it is ready.

Answer 1

Base diameter = 7 cm
Radius of the base = $\frac{7}{2}\mathrm{cm}$
Height of the cylinder = 20 cm

Curved/lateral surface area of the cylinder $=2\pi rh=\left(2\times \frac{22}{7}\times \frac{7}{2}\times 20\right){\mathrm{cm}}^2=440{\mathrm{cm}}^2$

Curved surface area of hemisphere$=2{\mathrm{\pi r}}^2$
Therefore, curved surface area of two hemispheres$=2\times 2{\mathrm{\pi r}}^2=\left(2\times 2\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\right){\mathrm{cm}}^2=154{\mathrm{cm}}^2$

Total surface area of the article $=\left(440+154\right){\mathrm{cm}}^2=594{\mathrm{cm}}^2$