Question

A juice seller was serving his customers using glass. The inner diameter of the cylindrical glass was 5 \ cm5 cm , but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of the glass was 12 cm, find what the apparent capacity of the glass was and what the actual capacity was

Answer 1

Find the volume of the cylinder:

Volume = πr²h

Volume = π(5 ÷ 2)²(12) = 15π cm³

Find the volume of the hemisphere:

Volume = 2/3 πr³

Volume = 2/3 π(5 ÷ 2)³ = 18π cm³

Find the capacity of the glass:

Capacity = 18π - 15π =3π =9.42cm³

Answer: Its actual capacity is 9.42 cm³

Answer 2

Find the volume of the cylinder:

Volume = πr²h

Volume = π(5 ÷ 2)²(12) = 15π cm³

Find the volume of the hemisphere:

Volume = 2/3 πr³

Volume = 2/3 π(5 ÷ 2)³ = 18π cm³

Find the capacity of the glass:

Capacity = 18π - 15π =3π =9.42cm³

Answer: Its actual capacity is 9.42 cm³