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. 

Answer 1

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