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Question 27
If the radius of a right circular cylinder is decreased by 20% while its height is increased by 40%, then the percentage change in its volume will be:
Solution
Volume of right circular cylinder = $$\pi r^2 h$$
Now,
$$r_1 = 0.8r$$
$$h_1 = 1.4h$$
Volume of right circular cylinder = $$\pi (0.8h)^2 \times 1.4h = 0.896\pi r^2 h$$
Decrement in volume = $$\pi r^2 h - 0.896\pi r^2 h = 0.104\pi r^2 h$$
Percentage decrement in volume = $$\frac{0.104\pi r^2 h}{\pi r^2 h} \times$$ 100 = 10.4%
$$\therefore$$ The correct answer is option B.
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