Question

A solid metallic sphere of radius 5.6 cm is melted and solid cones each of radius 2.8 cm and height 3.2 cm are made. Find the number of such cones formed.

Answer 1

Let the number of such cones formed be n
Now, Volume of solid metallic sphere = Volume of n solid cones

Let n be the number of cones,

Volume of cube = n $\times$ volume of one cone

=> $\frac{4}{3}\pi r^3=n\times \frac{1}{3}\pi r^{2}h$

=> $\frac{4}{3}\times \frac{22}{7}\times (5.6{)}^3=n\times \frac{1}{3}\times \frac{22}{7}\times (2.8{)}^2\times 3.2$

=> $4\times (5.6{)}^3=n\times (2.8{)}^2\times 3.2$

=> $r=28$