Sum

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

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#### Solution

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"`

Concept: Frustum of a Cone

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