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Question

A vessel is in the form of hemispherical bowl surmounted by a hollow cylinder of the 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 are of the vessel.[Use π=227]

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Solution

Let the radius and height of cylinder is r cm and h cm respectively.

Diameter of the hemisphere bowl =14 cm

Radius of the hemispherical bowl = Radius of the cylinder =r=142 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 cm7 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(2πrh+2πr2)=4πr(h+r)=4×227×7×(6+7)cm2
=88×13
=1144 cm2
Thus, the total surface area of the vessel is 1144 cm2.


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