Question

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

Answer 1

Diameter of hemisphere $=$ side of cube $=7cm$

Surface area $=5\times (7{)}^2+7^2-\pi {\left(\frac{7}{2}\right)}^2+2\pi {\left(\frac{7}{2}\right)}^2$

$6\times (side{)}^2$ projection of Hemisphere

hemisphere area area

$=6\times 49+\frac{\Pi \times 49}{4}=49(\frac{\pi }{4}+6)c{m}^2$

Hence, this is the answer.