Question

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

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Answer 1

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Volume of vessel = πr^2h + 2/3πr^3

= πr^2(h+2/3r)

= 22/7 × 3.5 × 3.5(14/3+2/3×3.5)

= 22×0.5×3.5(14/3+7/3)

= 11×3.5(21/3)

= 38.5×7

= 269.5m^3

surface area = 2πrh+2πr^2

=2πr(h+r)

= 2×22/7×3.5(14/3+3.5)

= 44×0.5(24.5/3)

= 22 × 24.5/3

= 539/3

=179.66m^2

Answer 2

Answer:

The Volume of the vessel , V = 56 m³  and the internal surface area of the solid ,S = 70.58 m³

Step-by-step explanation:

SOLUTION :  

Given :  

Diameter of the hemisphere = 3.5 m

Radius of the hemisphere , r = 3.5/2 = 1.75 m

Height of the cylinder , h  = 14/3 m

Total volume of the vessel = volume of the cylinder + volume of the  hemisphere

V = πr²h + 2/3 πr³

V = πr²(h + 2/3 r)

V = 22/7 × (1.75)² (14/3+ 2/3 × 1.75)

V = 67.375/7 (14/3 + 3.5/3)

V = 9.625 (17.5/3)

V = 168.4375/3  

V = 56 m³

Hence,the Volume of the vessel , V = 56 m³

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

S = 2πrh + 2πr²

S = 2πr(h + r)

S = 2π ×1.75 (14/3 + 1.75)

S = 2 × 22/7 × 1.75 [(14+ 15.25)/3]

S = 44 × 0.25 [19.25/3]

S = 11 × 6.416

S = 70.58 m³

Hence, the Volume of the vessel , V = 56 m³  and the internal surface area of the solid ,S = 70.58 m³

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