QQuestion
A solid wooden capsule consists of a cylindrical block and two hemispheres, as shown. Find the sum of the total surface areas of the three separate parts shown in Figure 2. The radius is 3.5 cm and the cylindrical block is 14 cm long.
(Use \frac{22}{7})
✓Answer
Radius, r = 3.5 cm
Height of cylinder, h = 14 cm
Total surface area of the cylinder = 2πr(h + r)
Total surface area of one hemisphere = 3πr²
Sum of the total surface areas of all three parts:
= 2πr(h + r) + 2(3πr²)
= 2πrh + 2πr² + 6πr²
= 2πrh + 8πr²
= 2πr(h + 4r)
Substituting the values:
= 2 × \frac{22}{7} × 3.5 × (14 + 4 × 3.5)
= 22 × (14 + 14)
= 22 × 28
= 616 cm²
Therefore, the required surface area is 616 cm².
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