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Question 10
The radius of the base of a right circular cylinder is increased by 20%. By what per cent should its height be reduced so that its volume remains the same as before?
Solution
Let the height be reduced by x%.
r1 = 1.2r
h1 = $$\frac{(100 - x)h}{100}$$
Volume of right circular cylinder = $$\pi r^2 h$$
$$\pi r^2 h = \pi (r1)^2 h1$$
$$r^2 h = (1.2r)^2 \times \frac{(100 - x)h}{100}$$
100 = 1.44(100 - x)
1.44x = 44
x = $$\frac{44}{1.44} = 30 \frac{5}{9}$$
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