Ex 12.2, 1 - Chapter 12 Class 10 Surface Areas and Volumes

Transcript

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