A solid metallic cylinder of height 10 cm and radius 6 cm is melted to make two cones in the ratio o...........

Quantitative Aptitude (CDS) Mensuration 3D

A solid metallic cylinder of height 10 cm and radius 6 cm is melted to make two cones in the ratio of volume 1:2 and of same height as 10 cm . What is the percentage increase in the flat surface area?

25%

50%

75%

100%

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Explanation:

Volume of cylinder = $\pi$ r²h = $\pi$ 6²10 = 360 $\pi$
Volume of first cone = 120 $\pi$
and volume of second cone = 240 $\pi$
for cone 1 v1= 1/3 $\pi$ r₁²10=120 $\pi$ => r₁= 6
for cone 2 v2= 1/3 $\pi$ r₂²10=240 $\pi$ => r₂= 6 $\sqrt{2}$
old flat area = 2 $\pi$ 6² = 72 $\pi$
New flat area = $\pi$ 6²+ $\pi$ (6 $\sqrt{2}$ )²= 108 $\pi$
% increase = 36 $\pi$ /72 $\pi$ x100= 50%