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Deepak Bora
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A solid toy is in the form of a hemisphere surmounted by a right circular cone of same radius. The height of the cone is 10 cm and the radius of the base is 7 cm. Determine the volume of the toy. Also find the area of the coloured sheet required to cover the toy. [ Use π = 22/7 and √149 = 12.2

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CBSE 10th Class Mathematics
Past year question paper
Year 2020
SET 1, Code Number  – 30/5/1
Question Number –  38
hemisphere surmounted by a right circular cone of same radius
cone area and volume problem

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1 Answer

  1. Volume of the toy = Volume of cone + Volume of hemisphere

    Cone: r = 7 cm, h = 10 cm

    Hemisphere: r = 7 cm

    Volume of toy = [1/3 (πr²h)] + [2/3 (πr³)]

    = { 1/3 (πr² [h+ 2r] ) }

    = { 1/3 (22 × 7 × 24 ) }

    Volume of toy = 1232 cm³

    Area of coloured sheet required to cover the toy = CSA of cone + CSA of hemisphere

    = πrl + 2πr²

    = πr [ l + πr ]

    = [22 / 7] × 7 [12.2 + 14]

    l² = 10² + 7²

    l =  100 + 49

    l = √149

    l =12.2

    = 22 × 26.22

    = 576.4 cm²

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