Question

Question 4
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.

Answer 1

The greatest diameter = side of the cube = 7 cm
Total surface area of solid = Surface area of cube – Surface area of base of hemisphere + Curved surface area of hemisphere
Surface area of cube $=6\times sid{e}^2$
$=6\times 7\times 7=294$ sq cm
Surface area of base of hemisphere
$=\pi r^2$
$=\frac{22}{7}\times {3.5}^2=38.5c{m}^2$
Curved surface area of hemisphere $=2\times 38.5=77$ sq cm
Total surface area $=294–38.5+77=332.5$ sq cm