Question

A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast. 

Answer 1

Radius of a solid sphere = R = 15 cm

∴ Volume of sphere melted = `4/3piR^3`

= `4/3 xx pi xx 15 xx 15 xx 15`

Radius of each cone recasted = r = 2.5 cm

Height of each cone recasted = h = 8 cm

∴ Volume of each one cone recasted = `1/3pir^2h`

= `1/3 xx pi xx 2.5 xx 2.5 xx 8`

∴ Number of cones recasted = `"Volume of sphere melted"/"Volume of each cone formed"`

= `(4/3 xx pi xx 15 xx 15 xx 15)/(1/3 xx pi xx 2.5 xx 2.5 xx 8)`

= 270