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Deepak Bora
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A toy is in the shape of a cone mounted on a hemisphere of same base radius. If the volume of the toy is 231 cm³ and its diameter is 7 cm, then find the height of the toy

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This is the important question that question was asked in 2012 cbse board exam. In this question a toy is in the shape of a cone mounted on a hemisphere. Question from RS Aggarwal Chapter Mensuration  Volume and Surface Area of Solid Exercise 17A Page number 786 problem number 15

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1 Answer

  1. Given data :-

    Volume of toy = 231 cm³

    Diameter of hemisphere = 7 cm

    radius of hemisphere = radius of cone = 3.5 cm

    Height of hemisphere= radius of hemisphere= 3.5 cm

    height of the toy = H

    height of the cone = h

    ∴ H= height of cone+ height of hemisphere

    H = h + r

    H = h + 3.5

    volume of toy = volume of cone + volume of hemisphere

    volume of toy

    = [1/3]πr²h + [2/3]πr³

    = πr²/3(h+2r)

    (22/7) × (3.5)² × (1/3) (h+2 × 3.5) = 231

    ( 22 × 3.5 × 3.5) / 7 (h+7) = 231 × 3

    (231 × 3 × 7) / (3.5× 3.5 × 22) = (h+7)

    (3×3)/(0.5×0.5×2)=h+7

    900 /50 = h+7

    18 = h+7

    h = 18-7

    h = 11 cm

    Height of toy = h+r

    = 11+3.5

    = 14.5

    ∴ height of the toy = 14.5 cm

    Answer wrong in the book refer this

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