-
The outer and inner radii of a hollow metallic cylinder of height 24 cms. are respectively 6.75 cms. and 5.25 cms. It is melted to form a solid sphere. Find the surface area of the sphere.
-
- π × (12)²/3 sq. cm
- π × 36 × (12)²/3 sq. cm
- 1220 sq. cm
- π × 36 × (12)²/3 sq. cm
- π × (12)²/3 sq. cm
Correct Option: B
Volume of metallic cylinder
= π(r1² - r2²) × h
= π(6.752 – 5.252) × 24 = π × 12 × 1.5 × 24 cu.cm.
∴ Volume of sphere = π × 12 × 1.5 × 24
| ⇒ | πr³ = π × 12 × 1.5 × 24 | |
| 3 |
| ⇒ r³ = | = 12 × 3 × 3 × 3 | |
| 4 |
∴ r = ³√12 × 3 × 3 × 3
= 3³√12
∴ Surface area = 4πr²
= 4 × π × (3³√12)²
= 4 × π × 9 (12)²/3
= π × 36 (12)²/3 sq.cm.
