The cubical block of side 7 cm is surmounted by a hemisphere of the largest size. Find the surface area of the resulting solid.
The cubical block of side 7 cm is surmounted by a hemisphere of the largest size. Find the surface area of the resulting solid.

Since, the diameter of the largest hemisphere that can be placed on a face of a cube of side 7 cm will be 7 cm.

radius = r = 7/2 cm

It’s curved surface area = 2 πr2 = 2 x 22/7 x 7/2 x 7/2 = 77 cm2 …… (i)

Now,

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

Selina Solutions Concise Class 10 Maths Chapter 20 ex. 20(E) - 3

Surface area of the cube = 5 x (side)2 = 5 x 49 = 245 cm2 …… (iii)

Hence,

Total area of resulting solid = 245 + 10.5 + 77 = 332.5 cm2