CAT 2017 Slot 1 — QA Question 19
SphereEasy
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 9π cm3. Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder is:
Answer & solution
Answer: 6
Solution
The height of the cylinder (h) = 3
The volume = 9π
⇒ πr2h = 9π
⇒ r = √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.
Hence, 22 = a2 + (√3)2
∴ a = 1
∴ The height of the topmost point of the ball from the base of the cylinder is = height of cylinder + height of center of ball from the top of cylinder + radius of the ball = 3 + 1 + 2 = 6.
Hence, 6.