Ex 12.2, 1
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π.
Now,
Total volume of the solid
= Volume of cone + Volume of hemisphere
Volume of cone
Here, Radius = r = 1 cm
& Height = h = 1 cm
Volume of cone = 1/3 πr2h
= 1/3 π × (1)2 × (1)
= 𝟏/𝟑 𝛑 cm3
Volume of hemisphere
Radius = r = 1 cm
Volume of hemisphere = 2/3 𝜋𝑟3
= 2/3 𝜋(1)3
= 𝟐/𝟑 𝝅 cm3
Now,
Total volume of solid = Volume of cone + Volume of hemisphere
= 𝟏/𝟑 𝝅 + 𝟐/𝟑 𝝅
= 3/3 𝜋
= 𝝅 cm3
Hence, total volume of solid is 𝜋 cm3

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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