Q12 of 180 Page 3

A hemispherical depression is taken out from a cube with the side ‘2a’. The total surface area of the solid is __________.


Total Surface Area = TSA of cube – Area of hemisphere base + CSA of Hemisphere


⇒ 6(2a)2 – πr2 + 2πr2 [1]


Here, diameter of hemisphere = side of cube = 2a


⇒ radius of hemisphere = 1/2 × diameter = ‘a’


Simplifying equation [1] and putting r = ‘a’, we have


⇒ Total Surface Area = 24a2 + πa2


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