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The radius of a cylinder is 10 cm and height is 4 cm. The number of centimetres that may be added either to the radius or to the height to get the same increase in the volume of the cylinder is
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- 5 cm
- 4 cm
- 25 cm
- 16 cm
- 5 cm
Correct Option: A
Let radius be increased byx cm. then Volume of cylinder = π(10 + x)² × 4
Again, let height be increased by x cm.
then Volume of cylinder = π × 10² (4 + x)
∴ π (10 + x)² × 4 = π (10)² (4 + x)
⇒ π(10 + x)² = 25 (4 + x)
⇒ 100 + 20x + x² = 100 + 25x
⇒ x² – 5x = 0
⇒ x (x – 5) = 0
⇒ x = 5 cm