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Deepak Bora
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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.

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An Important Question of class 10 Based on Mensuration Chapter of M.L Aggarwal for ICSE BOARD.
This figure shows a hemisphere with given radius and surmounted by a right circular cone of base radius given. Find the volume of the solid if the height of the cone is given.
This is the Question Number 14, Exercise 17.4 of M.L Aggarwal.

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1 Answer

  1. 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)r3 + (1/3)r2h

    = (1/3)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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