Question

A cubical block of side $7cm$ is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.

Answer 1

As per the question we can draw the diagram,
The diagram shows that the greatest diameter possible for such hemisphere is equal to the length of cube edge, i.e., $7$cm.
Radius $\left(r\right)$ of hemispherical part $=\frac{7}{2}$ $=3.5$cm

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

$=6(Edge{)}^2+2\pi r^2-\pi r^2=6(Edge{)}^2+\pi r^2$

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

$=294+38.5$

$=332.5$ $c{m}^2$