A container shaped like a right circular cylinder having base radius 6 cm and height 15 cm is full of ice-cream. The ice-cream is to be filled into cones of height 12 cm and radius 3 cm, having a hemispherical shape on the top. Find the number of such comes which can be filled with ice-cream.

We have

Let radius of cylinder be denoted by r, radii of cone and hemisphere are same and be denoted by r₁; height of the cylinder be denoted by h and height of the cone be denoted by h₁.

Given that, h = 15 cm, r = 6 cm, h₁ = 12 cm and r₁ = 3 cm.

We know the volume of cylinder = πr²h

And volume of ice-cream cone = 1/3 πr₁²h₁

And volume of hemispherical cone = 2/3 πr₁³

Number of cones that can be filled with ice-cream is given by

.

⇒

⇒

Thus, the number of cones that can be filled with ice-cream is 10.