Question

The volume of a cone varies as the square of the
radius of its base when its height is fixed and also
varies as its height when radius of its base is fixed.
If a radius of 3 cm and height of 7 cm give it a
volume of 66 cubic centimetre, then what will be the
radius, (in centimetres), if the cone has a height of
6 cm and volume of 308 cubic centimetres?

Answer 1

Answer: 7

Step-by-step explanation:

The volume of a cone varies as the square of the  radius of its base when its height is fixed and also  varies as its height when radius of its base is fixed.

V∝r²h⇒ V=k.r²h⇒ k=V/r²h

Let V1 = 66, r1 = 9 and h1 = 7 similarly,

     V2 = 308, r2 = ? and h2 = 6

k= V1 / ( (r1)² * h1) = V2 / ( (r2)² * h2)

Hence, 66 / (9 × 7) = 308 / (6 × (r2)²)

r2 =7