Q19 of 46 Page 1

A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting total surface area of the solid so formed, at the rate of rs. 5 per 100 sq. cm. (use π = 3.14)

Side of cubical block, a = 10 cm


Largest diameter that the hemisphere can have, d = 10 cm


Radius, r = 10/2 = 5 cm


Total surface area = Total surface area of cube + CSA of hemisphere - Area of base of hemisphere


= 6a2 + 2πr2 - πr2


= 6a2 + πr2


= 6(5)2 + 3.14(5)2


= 150 + 78.5 = 228.5 cm2


Rate for 100 cm2 painting = RS 5


Rate for 228.5 cm2 painting =



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