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Question
A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylindrical part is `4 2/3` m and the diameter of hemisphere is 3.5 m. Calculate the capacity and the internal surface area of the vessel.
Solution
Diameter of the base = 3.5 m
Therefore, radius =`3.5/2 m = 1.75 m = 7/4 m`
Height of cylindrical part = `4 2/3 = 14/3 m `
(i) Capacity (volume) of the vessel
= `pir^2h + 2/3pir^3`
= `pir^2(h + 2/3r)`
= `22/7 xx 7/4 xx 7/4(14/3 + 2/3 xx 7/4)`
= `77/8(14/3 + 7/6)`
= `77/8((28 + 7)/6)`
= `77/8 xx 35/6`
= `2695/48`
= 56.15 m3
(ii) Internal curved surface area
= `2pirh + 2pir^2 = 2pir(h + r) `
= `2 xx 22/7 xx 7/4(14/3 + 7/4)`
= `11((56 + 21)/12)`
= `11 xx 77/12`
= `847/12`
= 70.58 m2
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