Question

A solid metallic sphere of radius 10.5 cm is melted and recast into a number of smaller cones, each of radius 3.5 cm and height 3 cm. Find the number of cones so formed.

Answer 1

Volume of sphere $=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times (10.5{)}^3=4851c{m}^3$
Now,
Volume of one cone $=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}\times (3.5{)}^2\times 3=38.5c{m}^3$

Total number of cones = Volume of metallic sphere $÷$ volume of one cone
$=\frac{4851}{38.5}$
= 126 cones
Total number of cones can be formed is 126