Question

A solid sphere of radius $15$cm is melted and recast into solid right circular cones of radius $2.5$cm and height $8$cm. Calculate the number of cones recast.

Answer 1

Radius of sphere $R=15cm$

Dimensions of cone $r=2.5cmh=8cm$
When a solid is converted from one form to another, the amount of volume remains the same. Let $x$ number of cones can be melted.

Number of cones, $x=\frac{\text{Volume of sphere}}{\text{Volume of 1 cone}}$

$=\frac{\frac{4}{3}\pi (15{)}^3}{\frac{1}{3}\pi \left(2.5{)}^2\right(8)}=\frac{4(15{)}^3}{(2.5{)}^{2}8}=270cones$