Example
Ex 1:
Find the curved and total surface areas of a hemisphere of radius 21 cm.
Sol:
| Radius of the hemisphere(r) | = | 21 cm |
| The Curved surface area of the hemisphere | = | 2πr2 |
| = | 2 ⨯  ⨯ (21)2 |
|
| = | 2 ⨯ ⨯ 21 ⨯ 21 |
|
| = | 2772 cm2 | |
| Total surface area of hemisphere | = | 3πr2 |
| = | 3 ⨯ ⨯ (21)2 |
|
| = | 3 ⨯ ⨯ 21 ⨯ 21 |
|
| = | 4158 cm2 |
Ex 2:
A hemispherical bowl made of brass has an inner diameter of 14cm. Find the cost of tin–plating on the inside at the rate of ₹20 per 100 cm2
Sol:
| Inner diameter of the hemispherical bowl | = | 14 cm |
| Radius (r) | = | d/2 = 14/2 = 7 cm |
| = | 2 ⨯ ⨯ (7)2 |
|
| = | 2 ⨯ ⨯ 7 ⨯ 7 |
|
| = | 308 cm2 | |
| The cost of tin–plating it on the inside at the rate of ₹20 per 100 cm2 | ||
| = | 308 ⨯ 20 per 100 cm2 | |
| = | ₹ 6160/100 | |
| = | ₹ 61.6 | |