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ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.4 in Chapter 17 - Mensuration
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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.
Answer:
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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