Question

A cylindrical container is filled with ice-cream. Its diameter is 12cm and height is 15cm. The whole ice-cream is distributed among 10 children in equal cones having hemispherical tops. If the height of the conical portion is twice the diameter of its base, find the diameter of the ice-cream cone.

Answer 1

Let the radius of the base of conical ice cream = x cm

Then, height of the conical ice cream = 2 × diameter

= 2 × (2x)

= 4x cm

Volume of ice- cream cone

= Volume of conical portion + Volume of hemispherical portion

= 2πx³ cm³

Now,

Diameter of cylindrical container = 12cm

So, radius = 6cm

and height = 15cm

∴ Volume of cylindrical container = πr²h

= π × (6)² × (15)

= 540π cm³

⇒ x³ = 27

⇒ x = 3

So, the radius of the base of conical ice cream is 3cm

Hence, the diameter of the base of conical ice-cream = 2×3 = 6cm