A solid wooden capsule is shown in Figure 1. The capsule is formed of a cylindrical block and two hemispheres.
Find the sum of total surface area of the three parts as shown in Figure 2. Given, the radius of the capsule is 3.5 cm and the length of the cylindrical block is 14 cm.
(Use $\pi = \frac{22}{7}$)
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From figure,
Radius of cylindrical block = radius of hemispheres = r = 3.5 cm
Height of cylindrical block = h = 14 cm.
By formula,
Total surface area of cylinder = 2πr(h + r)
Total surface area of a hemisphere = 3πr2
Total surface area = Total surface area of cylinder + Total surface area of 2 hemispheres
= 2πr(h + r) + 2 × 3πr2
= 2πrh + 2πr2 + 6πr2
= 2πrh + 8πr2
= 2πr(h + 4r).
Substituting values, we get :
$$\begin{aligned}\text{Total surface area} = 2 \times \frac{22}{7} \times 3.5 \times (14 + 4 \times 3.5) \\[1em] = 2 \times 22 \times 0.5 \times (14 + 14) \\[1em] = 22 \times 28 \\[1em] = 616 \text{ cm}^2.\end{aligned}$$
Hence, the total surface area = 616 cm2.