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A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is 14/3 and the diameter of the hemisphere is 3.5 m. Calculate the volume and the internal surface area of the solid.

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In this question we have to calculate the volume
and the internal surface area of the solid,From a
vessel is a cylinder fitted with a hemispherical bottom of
the same base. The depth of the cylinder is 14/3
and the diameter of the hemisphere is 3.5 m.

This question is from r d sharma class 10 maths.
I found this question while doing mensuration of
class 10.
I need help in getting the solution.

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1 Answer

  1. Given,

    Diameter of the hemisphere = 3.5 m

    So, the radius of the hemisphere (r) = 1.75 m

    Height of the cylinder (h) = 14/3 m

    We know that, volume of the Cylinder = πr2 h1 = V1

    V1 = π(1.75)2 x 14/3 m3

    The volume of the hemispherical bottom = 2 × 2/3 × 22/7 × r3 = V2

    V2 = 2/3 × 22/7 × 1.753 m3

    Therefore,

    The total volume of the vessel (V) = volume of the cylinder + volume of the hemisphere

    V = V1 + V2

    V = π(1.75)2 x 14/3 + 2/3 × 22/7 × 1.753

    V = π(1.75)2 (14/3 + 2/3 x 1.75)

    V = 56.15 m2

    Hence, the volume of the vessel = V = 56.15 m3

    Now,

    Internal surface area of solid (S) = Surface area of the cylinder + Surface area of the hemisphere

    S = 2 πr h1 + 2 πr2

    S = 2 π(1.75)(143) + 2 π(1.75)2

    S = 70.51 m3

    Therefore, the internal surface area of the solid is 70.51 m3

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