Question

A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid. [Use `pi = 22/7`]

Answer 1

From the figure, it can be observed that the greatest diameter possible for such hemisphere is equal to the cube’s edge, i.e., 7cm.

Radius (r) of hemispherical part = `7/2` = 3.5 cm

Total surface area of solid = Surface area of cubical part + CSA of hemispherical part − Area of base of hemispherical part

= 6 (Edge)² + 2πr² - πr²  

= 6 (Edge)² + πr²

Total surface area of solid = `6(7)^2 + 22/7 xx 7/2xx 7/2`

= 294 + 38.5

= 332.5 cm²