A hemispherical bowl of internal diameter 24 cm is full of a liquid. This liquid is to be filled into cylindrical bottles each of radius 4 cm and height 18 cm. How many such bottles are required to empty the bowl?

Question

Question

This question was previously asked in

SSC MTS (2022) Official Paper (Held On: 19 Jun, 2023 Shift 2)

Answer 1

Given:

Internal diameter of hemispherical bowl = 24 cm

The radius of the cylindrical bottle = 4 cm

Height of the cylindrical shaped bottle = 18 cm

Concept :

Volume of hemispherical bowl = n x Volume of one cylindrical-shaped bottle

Calculations:

Let the number of bottles be n.

Internal radius of hemispherical bowl = 12 cm

Volume of hemisphere = 2/3πr³

⇒ 2/3 × π × 12 × 12 × 12

⇒ 2 × π × 12 × 12 × 4

⇒ 1152 π

Volume of cylinder = πr²h

⇒ π × 4 × 4 × 18

⇒ 288π

According to the question :

Volume of hemispherical bowl = n x Volume of one cylindrical-shaped bottle

1152π = n x 288π

n = 4

Hence, the required number of cylinders is 4.