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 = `1/3pir^2h` 

= `1/3 xx pi xx 6 xx 6 xx 8` 

= 96π cm³ 

Height of smaller cone = 2 cm 

And radius = `1/2` cm 

Volume of smaller cone

= `1/3 xx pi xx 1/2 xx 1/2 xx 2`  

= `1/6pi  cm^3` 

Number of cones so formed  

= `(96pi)/(1/6pi)` 

= `96pi xx 6/pi` 

= 576