Example 6
A juice seller was serving his customers using glasses as shown in figure. The inner diameter of the cylindrical glass was 5 cm, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was 10 cm, find the apparent capacity of the glass and its actual capacity. (Use π= 3.14.)
Now,
Apparent capacity of the glass = Volume of cylinder
And,
Actual capacity of the glass
= Volume of cylinder – Volume of hemisphere
Volume of cylinder
Given inner diameter of the glass = 5 cm
So, radius = r = 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟/2 "=" 5/2 = 2.5 cm
Height = 10 cm
Volume of cylinder
Given Inner diameter of the glass = 5 cm
So, radius = r = 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟/2 "=" 5/2 = 2.5 cm
Height = h = 10 cm
Now,
Volume of the cylindrical glass = 𝜋𝑟2ℎ
= 3.14 ×(2.5)2 ×10
= 3.14 × 2.5 × 2.5 ×10
= 3.14 × 6.25 × 10
= 196.25 cm3
Volume of the hemisphere
Radius of hemisphere = r = 2.5 cm
Volume of the hemisphere = 2/3 πr3
= 𝟐/𝟑 × 𝟑.𝟏𝟒 × (𝟐.𝟓)𝟑
= 2/3×3.14×2.5×2.5×2.5
= 2/3×3.14×15.62
= 32.7 cm3
Now,
Apparent capacity of glass = Volume of cylinder = 196.25 cm3
And,
Actual capacity of the glass
= Total volume of cylinder – volume of hemisphere
= 196.25 – 32.7
= 163.54cm3
Hence,
Apparent capacity = 196.25cm3
Actual capacity of the glass = 163.54cm3

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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