Question

A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius 1.5 cm and height 4 cm. How many bottles are needed to empty the bowl?

Answer 1

Let n bottles are needed to empty the bowl,

Therefore,

Volume of bowl = Volume of 'n' bottles

For hemispherical bowl,

Radius, r = 9 cm

As we know,

Volume of a hemispherical bowl = 2/3πr³

Where r is the radius of hemisphere

Volume of bowl

For single cylindrical bottle,

Base radius, r = 1.5 cm

Height, h = 4 cm

As we know,

Volume of cylinder = πr²h

Where r is base radius, h is height of cylinder.

Volume of one bottle = π(1.5)²(4) = 9π cm³

As,

Volume of bowl = volume of n bottles

486π = (9π)n

n = 486/9 = 54

Hence, 54 bottles are needed to empty the bowl.