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.
Answers
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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:
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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