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A tent of height 77 dm is in the form of a right circular cylinder of diameter 36 m and height 44 dm surmounted by a right circular cone. Find the cost of the canvas at Rs. 3.50 per m2

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If you open math book you will find a lot of mathematical questions but
youshould have solve this question.
It is from class 10 rd sharma chapter 16 mensuration .

In this question we have to find the the cost of the canvas at Rs. 3.50 per m2
given that a tent of height 77 dm is in the form of a right circular cylinder
of diameter 36 m and height 44 dm surmounted by a right circular cone.

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1 Answer

  1. Given,

    Height of the tent = 77 dm

    Height of a surmounted cone = 44 dm

    Height of the Cylindrical Portion = Height of the tent – Height of the surmounted Cone

    = 77 – 44

    = 33 dm = 3.3 m

    And, given diameter of the cylinder (d) = 36 m

    So, its radius (r) of the cylinder = 36/2 = 18 m

    Let’s consider L as the slant height of the cone.

    Then, we know that

    L2 = r2 + h2

    L2 = 182 + 3.32

    L2 = 324 + 10.89

    L2 = 334.89

    L = 18.3 m

    Thus, slant height of the cone (L) = 18.3 m

    Now, the Curved Surface area of the Cylinder (S1) = 2πrh

    S1 = 2π (184.4) m2

    And, the Curved Surface area of the cone (S2) = πrL

    S2 = π × 18 × 18.3 m2

    So, the total curved surface of the tent (S) = S1 + S2

    S = S1 + S2

    S = (2π18 × 4.4) + (π18 × 18.3)

    S = 1533.08 m2

    Hence, the total Curved Surface Area (S) = 1533.08 m2

    Next,

    The cost of 1 m2 canvas = Rs 3.50

    So, 1533.08 m2 of canvas will cost = Rs (3.50 x 1533.08)

    = Rs 5365.8

     

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