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Question
A cubical block of side 7 cm is surmounted by a hemisphere of the largest size. Find the surface area of the resulting solid.
Solution
The diameter of the largest hemisphere that can be placed on a face of a cube of side 7 cm will be 7 cm.
Therefore, radius = r = `7/2` cm
Its curved surface area = 2πr2
= `2 xx 22/7 xx 7/2 xx 7/2`
= 77 cm2 ...(i)
Surface area of the top of the resulting solid = Surface area of the top face of the cube − Area of the base of the hemisphere
= `(7 xx 7) - (22/7 xx 49/4)`
= `49 - 77/2`
= `(98 - 77)/2`
= `21/2`
= 10.5 cm2 ...(ii)
Surface area of the cube = 5 × (side)2
= 5 × 49
= 245 cm2 ...(iii)
Total area of resulting solid = 245 + 10.5 + 77 = 332.5 cm2
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