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A tent is in the form of a cylinder of diameter 20 m and height 2.5 m, surmounted by a cone of equal base and height 7.5 m. Find the capacity of tent and the cost of the canvas at Rs 100 per square meter.

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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 capacity of tent and
the cost of the canvas at Rs 100 per square meter.From a tent
is in the form of a cylinder of diameter 20 m and height 2.5 m,
surmounted by a cone of equal base and height 7.5 m.

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1 Answer

  1. Given,

    Diameter of the cylinder = 20 m

    So, its radius of the cylinder (R) = 10 m

    Height of the cylinder (h1) = 2.5 m

    Radius of the cone = Radius of the cylinder (r) = 15 m

    Height of the Cone (h2) = 7.5 m

    Let us consider L as the slant height of the Cone, then we know that

    L2 = r2 + h22

    L2 = 152 + 7.52

    L2 = 225 + 56.25

    L2 = 281.25

    L = 12.5 m

    Now,

    Volume of the cylinder = πR2h1 = V1

    V1 = π(10)2 2.5

    V1 = 250 πm3

    Volume of the Cone = 1/3 × 22/7 × r2 × h22 = V2

    V2 = 1/3 × 22/7 × 102 × 7.5

    V2 = 250π m3

    So, the total capacity of the tent = volume of the cylinder + volume of the cone = V1 + V2

    V = 250 π + 250 π

    V = 500π m3

    Hence, the total capacity of the tent is 500π m3

    And, the total area of canvas required for the tent is S = 2 πRh1 + πrL

    S = 2(π)(10)(2.5) + π(10)(12.5)

    S = 550 m2

    Therefore, the total cost for canvas is (100) (550) = Rs. 55000

     

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