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A solid brass sphere of radius 2.1 dm is converted into a right circular cylindrical rod of length 7 cm. The ratio of total surface areas of the rod to the sphere is
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- 3 : 1
- 1 : 3
- 7 : 3
- 3 : 7
- 3 : 1
Correct Option: C
| Volume of copper sphere = | πr³ | |
| 3 |
| = | π(21)³ cu.cm. | |
| 3 |
Volume of cylindrical rod = πR²H = πR² × 7 cu. cm.
| ∴ πR² × 7 = | π × 21 × 21 × 21 | |
| 3 |
| ⇒ R² = | × | |||
| 3 | 7 |
∴ R = √4 × 21 × 21
= 2 × 21 = 42 cm.
Surface area of sphere = 4πr² = 4π(21)² sq. cm.
Total surface area of the rod = 2πR(R + H) = 2π × 42 (42 + 7)
= 2π × 42 × 49 sq. cm.
| ∴ Required ratio = | = 7 : 3 | |
| 4π × 21 × 21 |
