Question

A cylindrical vessel of height $32$cm and $18$cm as the radius of the base, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is $24$cm, the radius of its base is ___________.

• A. $12$cm
• B. $24$cm
• C. $36$cm
• D. $48$cm

Answer 1

Answer: (C)

$36$cm

Height of cylinder $=32$cm

Radius of cylinder $=9$cm

Volume of cylinder $=\pi {\left(9\right)}^2\left(32\right)$

It is emptied and the sand takes the shape of a cone.

Height of cone $=24$cm

Volume of cone $=\frac{1}{3}\pi r^2\left(24\right)$

But, volume of cone=volume of cylinder

$=>\pi {\left(9\right)}^2\left(32\right)=\frac{1}{3}\pi r^2\left(24\right)=>r^2={\left(18\right)}^2\times 4=>r=18\times 2=36cm$