1. A solid sphere of radius 9 cm is melted to form a sphere of radius 6 cm and a right circular cylinder of same radius. The height of the cylinder so formed is ?
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By: anil on 05 May 2019 01.48 am
Radius of original sphere = $$R=9$$ cm Radius of new sphere and cylinder = $$r=6$$ cm Let the height of cylinder = $$h$$ cm Volume of original sphere = Volume of new sphere + Volume of new cylinder => $$frac{4}{3} pi R^3=(frac{4}{3} pi r^3)+(pi r^2 h)$$ => $$frac{4}{3} imes (9)^3=(frac{4}{3} imes 6^3)+(6^2 imes h)$$ => $$972=288+36h$$ => $$36h=972-288=684$$ => $$h=frac{684}{36}=19$$ cm => Ans - (A)
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