Mathematics
A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylindrical part is m and the diameter of hemisphere is 3.5 m. Calculate the capacity and the internal surface area of the vessel.
Mensuration
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Answer
From figure,
Diameter of the base = 3.5 m
Radius of cylinder = Radius of hemispherical bottom = r = m = 1.75 m.
Height of cylindrical part (h) = m.
(i) Capacity (volume) of the vessel = Volume of cylinder + Volume of hemispherical bottom
Internal curved surface area = Surface area of cylindrical part + Surface area of hemispherical bottom
= 2πrh + 2πr2
= 2πr(h + r)
=
= 2 x 22 x 0.25 x (4.67 + 1.75)
= 2 x 22 x 0.25 x 6.42
= 70.62 m2.
Hence, volume of vessel = 56.15 m3 and internal curved surface area = 70.62 m2.
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