-
The total surface area of a metallic hemisphere is 1848 cm2. The hemisphere is melted to form a solid right circular cone. If the radius of the base of the cone is the same as the radius of the hemisphere, its height is
-
- 42 cm
- 26 cm
- 28 cm
- 30 cm
- 42 cm
Correct Option: C
Total curved surface area of hemisphere = 3πr²,
where r = radius of hemisphere.
∴ 3πr² = 1848
| ⇒ 3 × | × r² = 1848 | |
| 7 |
| ⇒ r² = | = 196 | |
| 3 × 22 |
⇒ r = √196 = 14 cm.
| Volume of hemisphere = | × π × 14 × 14 × 14 cm³ | |
| 3 |
| = | π cm³ | |
| 3 |
According to the question, Volume of cone = Volume of hemisphere
| ⇒ | πr²h = | π cm³ | ||
| 3 | 3 |
⇒ r²h = 5488
→ 14 × 14 × h = 5488
| ⇒ h = | = 28 cm | |
| 14 × 14 |
