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Consider a cylindrical tub having radius as 5 cm and its length 9.8 cm. It is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed in tub. If the radius of the hemisphere is 3.5 cm and the height of the cone outside the hemisphere is 5 cm, find the volume of water left in the tub.

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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-7 maths r d sharma,mensuration.

In this question we have to find the volume
of water left in the tub. Consider a cylindrical tub having
radius as 5 cm and its length 9.8 cm. It is full of water. A solid
in the form of a right circular cone mounted on a hemisphere is
immersed in tub. If the radius of the hemisphere is 3.5 cm and the
height of the cone outside the hemisphere is 5 cm.

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1 Answer

  1. Given,

    The radius of the Cylindrical tub (r) = 5 cm

    Height of the Cylindrical tub (H) = 9.8 cm

    Height of the cone outside the hemisphere (h) = 5 cm

    Radius of the hemisphere = 3.5 cm

    Now, we know that

    The volume of the Cylindrical tub (V1) = πr2H

    V1 = π(5)2 9.8

    V1 = 770 cm3

    And, the volume of the Hemisphere (V2) = 2/3 × π × r3

    V2 = 2/3 × 22/7 × 3.53

    V2 = 89.79 cm3

    And, the volume of the Hemisphere (V3) = 23 × π × r × 2h

    V3 = 2/3 × 22/7 × 3.52 × 5

    V3 = 64.14 cm3

    Thus, total volume (V) = Volume of the cone + Volume of the hemisphere

    = V2 + V3

    V = 89.79 + 64.14 cm3

    = 154 cm3

    So, the total volume of the solid = 154 cm3

    In order to find the volume of the water left in the tube, we have to subtract the volume of the hemisphere and the cone from the volume of the cylinder.

    Hence, the volume of water left in the tube = V1 – V2

    = 770 – 154

    = 616 cm3

    Therefore, the volume of water left in the tube is 616 cm3.

     

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