Question

A spherical cannon ball 28 cm in diameter is melted and recast into a right circular conical mould, base of which is 35 cm in diameter. Find the height of the cone.

Answer 1

Diameter of cannon ball = 28 cm
Radius of the cannon ball = 14 cm

Volume of ball `=4/3 pir^3 = 4/3pixx(14)^3 "cm"^3`

Diameter of base of cone = 35 cm

Radius of base of cone `=35/2 "cm"`

Let the height of the cone be h cm.

Volume of cone `= 1/3pir^2h = 1/3pixx(35/2)^2xx"h"  "cm"^3`

From the above results and from the given conditions,
Volume of ball = Volume of cone 

Or,`4/3pixx(14)^3 = 1/3pixx(35/2)^2xx"h"`

`rArr h = ((4/3)pixx(14)^3)/(1/3pi xx (35/2)^2 )=(4xx14xx14xx14xx2xx2)/(35xx35) = 35.84  "cm"`