Q. 204.3( 9 Votes )

A wooden article was made by scooting out a hemisphere from each end of a cylinder, as shown in the figure. If the height of the cylinder is 20 cm and its base is of diameter 7 cm, find the total surface area of the article when it is ready.


Answer :

The wooden article was made by scooting out a hemisphere from each end of a cylinder


Let the radius of cylinder be r cm and height be h cm.


Height of cylinder = h = 20 cm


Base diameter of cylinder = 7 cm


Base radius of cylinder = r = diameter ÷ 2 = 7/2 cm = 3.5 cm


Lateral Surface area of cylinder = 2πrh


= 2 × 22/7 × 3.5 × 20 cm2


= 2 × 22/7 × 3.5 × 20 cm2


= 440 cm2


Since, the wooden article was made by scooting out a hemisphere from each end of a cylinder


Two hemispheres are taken out in total


Radius of cylinder = radius of hemisphere


Radius of hemisphere = 3.5 cm


Lateral Surface area of hemisphere = 2πr2


= 2 × 22/7 × 3.5 × 3.5 cm2


= 77 cm2


Total Surface area of two hemispheres = 2 × 77 cm2 = 154 cm2


Total surface area of the article when it is ready = Lateral Surface area of cylinder + Lateral Surface area of hemisphere


Total surface area of the article when it is ready = 440 cm2 + 154 cm2


= 594 cm2


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