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A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of the cone are 6 cm and 4 cm, respectively. Determine the surface area of the toy.

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One of the important question for the board exam class 10 from
mensuration chapter.This question is from r d sharma class 10 maths.
chapter-16.2 question number-4 maths r d sharma,mensuration.

In this question we have to find the surface area of the toy,
givwn that a toy is in the form of a cone surmounted on a hemisphere.
The diameter of the base and the height of the cone are 6 cm and 4 cm, respectively.

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1 Answer

  1. Given that,

    The height of the cone (h) = 4 cm

    Diameter of the cone (d) = 6 cm

    So, its radius (r) = 3

    Let, ‘l’ be the slant height of cone.

    Then, we know that

    l2 = r2 + h2

    l2 = 32 + 42 = 9 + 16 = 25

    l = 5 cm

    Hence, the slant height of the cone (l) = 5 cm

    So, the curved surface area of the cone (S1) = πrl

    S1 = π(3)(5)

    S1 = 47.1 cm2

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

    S2 = 2π(3)2

    S2 = 56.23 cm2

    So, the total surface area (S) = S1 + S2

    S = 47.1 + 56.23

    S = 103.62 cm2

    Therefore, the curved surface area of the toy is 103.62 cm2

     

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