Question

A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5 cm. Find the number of spheres formed.

Answer 1

Radius of a solid cone (r) = 5 cm

Height of the cone = 8 cm

Volume of a cone  

= `1/3pir^2h` 

= `1/3 xx 5 xx 5 xx 8  cm^3` 

= `(200pi)/3 cm^3` 

Radius of each sphere = 0.5 cm 

∴ Volume of one sphere = `4/3pir^3` 

= `4/3 xx II xx 1/2 xx 1/2 xx 1/2 cm^3` 

= `(II)/6 cm^3` 

Number of spheres = `"Total volume"/"Volume of one sphere"` 

= `((200pi)/3)/(pi/6) xx 6/pi` 

= `(200pi)/3 xx 6/pi` 

= 400