Question

A solid cone of height 8 cm and base radius 6 cm is melted and recast into identical cones, each of height 2 cm and diameter 1 cm. Find the number of cones formed. 

Answer 1

Height of solid cone (h) = 8 cm

Radius (r) = 6 cm

Volume of solid cone = ${\displaystyle \frac{1}{3}\pi r^{2}h}$ 

= ${\displaystyle \frac{1}{3}\times \pi \times 6\times 6\times 8}$ 

= 96π cm³ 

Height of smaller cone = 2 cm 

And radius = ${\displaystyle \frac{1}{2}}$ cm 

Volume of smaller cone

= ${\displaystyle \frac{1}{3}\times \pi \times \frac{1}{2}\times \frac{1}{2}\times 2}$  

= ${\displaystyle \frac{1}{6}\pi c{m}^3}$ 

Number of cones so formed  

= ${\displaystyle \frac{96\pi }{\frac{1}{6}\pi }}$ 

= ${\displaystyle 96\pi \times \frac{6}{\pi }}$ 

= 576