# ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.4 in Chapter 17 - Mensuration

Question 20 Mensuration Exercise 17.4

The adjoining figure shows a hemisphere of radius 5 cm surmounted by a right circular cone of base radius 5 cm. Find the volume of the solid if the height of the cone is 7 cm. Give your answer correct to two places of decimal.

Solution:

The volume of the combined solids will equal the sum of the volumes of the separate solids.

Given radius of the hemisphere, r = 5 cm

Radius of cone, r = 5 cm

Height of the cone, h = 7 cm

Volume of the solid = Volume of the hemisphere + Volume of the cone

= (2/3)π r3 + (1/3)π r2h

= (1/3)π r2(2r+h)

= (1/3)×(22/7)×52(2×5+7)

= (22/21)×25(10+7)

= (22/21)×25×17

= 445.238 cm3

= 445.24 cm3

Hence the volume of the solid is 445.24 cm3 .

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