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A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

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I would like to give a question which
i could not solve.Rd sharma class 10
maths exercise-16.2 mensuration.

In this question we have to find the total surface
area of the toy given that a toy is in the form of
a cone of radius 3.5 cm mounted on a hemisphere of
same radius. The total height of the toy is 15.5 cm.

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1 Answer

  1. Given,

    Radius of the conical portion of the toy = 3.5 cm = r

    Total height of the toy = 15.5 cm = H

    If H is the length of the conical portion

    Then,

    Length of the cone (h) = H – r = 15.5 – 3.5 = 12 cm

    Now, we know that

    The curved surface area of the cone (S1) = πrL, where L is the slant height of the cone.

    L2 = r2 + h2

    L2 = 3.52 + 122

    L2 = 12.25 + 144 = 156.25

    L = 12.5

    So,

    S1 = π (3.5)(12.5)

    S1 = 137.5 cm2

    Next, the curved surface area of the hemisphere (S2) = 2πr2

    S2 = 2π (3.5)2

    S2 = 77 cm2

    Therefore,

    The total surface area of the toy (S) = Curved surface area of the cone + curved surface area of the hemisphere

    S = S1 + S2

    S = 137.5 + 77

    S = 214.5 cm2

    Hence, the total surface area of the children’s toy is 214.5 cm2

     

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