1. A cylinderical container of 32 cm height and 18 cm radius is filled with sand. Now all this sand is used to form a conical heap of sand. If the height of the conical heap is 24 cm, what is the radius of its base?
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By: anil on 05 May 2019 01.49 am
Let radius of base of cone = $$r$$ cm and height = $$h=24$$ cm Radius of cylinder = $$R=18$$ cm and height = $$H=32$$ cm Volume of cylinder = Volume of cone => $$pi R^2H=frac{1}{3} pi r^2h$$ => $$(18)^2 imes 32 = frac{1}{3} imes (r)^2 imes 24$$ => $$324 imes 32 = 8(r)^2$$ => $$r^2=324 imes frac{32}{8}$$ => $$r=sqrt{324 imes 4}$$ => $$r=18 imes 2=36$$ cm => Ans - (C)
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