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Question
A vessel is in the form of hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the total surface area of the vessel. `[\text{Use}pi=22/7]`
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Solution
Let the radius and height of cylinder be r cm and h cm respectively.
Diameter of the hemispherical bowl = 14 cm
∴ Radius of the hemispherical bowl = Radius of the cylinder = r = `14/2` cm = 7 cm
Total height of the vessel = 13 cm
∴ Height of the cylinder, h = Total height of the vessel − Radius of the hemispherical bowl
= 13 cm − 7 cm = 6 cm
Total surface area of the vessel = 2 (curved surface area of the cylinder + curved surface area of the hemisphere) (Twice because the vessel is hollow)
`=2(2pirh+2pir^2)=4pir(h+r)=4xx22/7xx7xx(6+7)cm^2`
`=1144 cm^2`
Thus, the total surface area of the vessel is 1144 cm2.
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