Ball Resting on Hollow Cylinder

CAT 2017 Slot 1 · QA · Hard · Mensuration and Geometry

All CAT 2017 Slot 1 questionsMore Mensuration and Geometry questionsAll CAT QA

A ball of diameter 4 cm4\text{ cm} is kept on top of a hollow cylinder standing vertically. The height of the cylinder is 3 cm3\text{ cm}, while its volume is 9π cm39\pi\text{ cm}^3. Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder is:

Answer

6

Explanation

Cylinder height h=3 cmh = 3\text{ cm}, volume πr2h=9π  ⟹  r2(3)=9  ⟹  r=3\pi r^2 h = 9\pi \implies r^2(3) = 9 \implies r = \sqrt{3}. Ball radius R=2 cmR = 2\text{ cm}. When sphere rests on top rim of radius r=3r = \sqrt{3}, the distance from center of sphere to top plane of cylinder is R2−r2=22−(3)2=1 cm\sqrt{R^2 - r^2} = \sqrt{2^2 - (\sqrt{3})^2} = 1\text{ cm}. Topmost point of ball is R=2 cmR = 2\text{ cm} above center of sphere. So topmost point is 1+2=3 cm1 + 2 = 3\text{ cm} above the top of the cylinder. Distance from base = cylinder height + 3 cm=3+3=6 cm3\text{ cm} = 3 + 3 = 6\text{ cm}.

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace