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A solid is composed of a cylinder with hemispherical ends. If the complete length of the solid is 104 cm and the radius of each of the hemispherical ends is 7 cm, find the cost of polishing its surface at the rate of Rs.10 per dm2.

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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 cost of
polishing its surface at the rate of Rs.10 per dm2.
Given that a solid is composed of a cylinder with
hemispherical ends. If the complete length of the
solid is 104 cm and the radius of each of the hemispherical ends is 7 cm.

 

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1 Answer

  1. Given,

    Radius of the hemispherical end (r) = 7 cm

    Height of the solid = (h + 2r) = 104 cm

    ⇒ h + 2r = 104

    ⇒ h = 104 − (2 × 7)

    So, h = 90 cm

    We know that,

    The curved surface area of the cylinder (S1) = 2 πr h

    S1= 2 π(7)(90)

    S1 = 3960 cm2

    Next,

    Curved surface area of the two hemisphere (S2) = 2 (2πr2)

    S2 = 2 x 2π(7)2

    S2 = 616 cm2

    Therefore,

    The total curved surface area of the solid (S) = Curved surface area of the cylinder + Curved surface area of the two hemispheres

    S = S1 + S2

    S = 3960 + 616

    S = 4576 cm2 = 45.76 dm2

    Given that the cost of polishing the 1 dm2 surface of the solid is Rs. 10

    So, the cost of polishing the 45.76 dm2 surface of the solid = Rs (10 x 45.76) = Rs. 457.6

    Therefore,

    The cost of polishing the whole surface of the solid is Rs. 457.60

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