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SSC CPO 2019 PYQ — Question 116

SSC CPO Tier I - 12th March 2019 - Shift 1 • Quantitative Aptitude • Q116

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A right circular cone of largest volume is cut from a solid wooden hemisphere. The remaining part is what percent of the volume of the original hemisphere?

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 50%

If a right circular cone of largest volume is cut out from a solid wooden hemisphere

then height of cone = Radius of hemisphere

Let h = height and r = radius

Volume of hemisphere(V) = (2/3)пr3

Volume of cone = (1/3)пr2h

But h = r

So, Volume of cone = (1/3)пr2h = (1/3)пr3 = V/2

Hence, Remaining material = V - V/2 = V/2 

Required percentage = [(V/2)/V] × 100 = 50%