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 $\pi =\frac{22 }{7}$]

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 = $\frac{7}{2}$ = 3.5cm
Total surface area of solid = Surface area of cubical part + CSA of hemispherical part − Area of base of hemispherical part$= 6×(Edge)^2+2\pi r^2-\pi r^2$
$= 6×(Edge)^2+\pi r^2$

$= 6×(7)^2+(\frac{22}{7})×(\frac{7}{2})×(\frac{7}{2})$

$= (6×49)+(\frac{77}{2})$

$= 294+38.5 = 332.5$ cm2