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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. 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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