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CAT 2017 [slot 1] Question with solution 19

Question 19:
A ball of diameter 4 cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is 3 cm, while its volume is $9\pi$ cubic centimeters. Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder is
Answer: 6
Explanation:

The height of the cylinder (h) = 3

The volume = $9 \pi$

$\pi r ^ { 2 } h = 9 \pi \Rightarrow r = \sqrt { 3 }$

The radius of the ball (R) = 2

The height of O, the centre of the ball, above the line representing the top of the cylinder is say a. (a = 1)

Therefore, the height of the topmost point of the ball from the base of the cylinder is h + a +R = 3 + 1 + 2 = 6


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