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A boiler which is in the form of a cylinder 2 m long with hemispherical ends each of 2 m diameter. Find the volume of the boiler.

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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-12 maths r d sharma,mensuration.

In this question we have to find the volume of the boiler given that
a boiler which is in the form of a cylinder 2 m long with hemispherical
ends each of 2 m diameter.

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1 Answer

  1. Given,

    Diameter of the hemisphere = 2 m

    So, the radius of the hemisphere (r) = 1 m

    Height of the cylinder (h1) = 2 m

    And, the volume of the Cylinder = πr2h1 = V1

    V1 = π(1)22

    V1 = 22/7 × 2 = 44/7 m3

    As at each of the ends of the cylinder, hemispheres are attached.

    So, totally there are 2 hemispheres.

    Then the volume of two hemispheres = 2 × 2/3 × 22/7 × r3 = V2

    V2 = 2 × 2/3 × 22/7 × 13

    V2 = 22/7 × 4/3 = 88/21 m3

    Thus,

    The volume of the boiler (V) = volume of the cylindrical portion + volume of the two hemispheres

    V = V1 + V2

    V = 44/7 + 88/21

    V = 220/21 m3

    Therefore, the volume of the boiler 220/21 m3

     

     

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