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

The hemisphere is mounted on the cubical block

The diameter of the hemisphere $=$ the side of the cube $=7cm$

$\Rightarrow TSA$ ofthe solid $=TSA$ of cube$-$ Area of base of hemisphere $+CSA$ ofhemisphere

$\Rightarrow TSA=(6\times 7^2)–(\pi \times (3.5{)}^2)+2(\pi \times \left(3.5{)}^2\right)$

$\Rightarrow TSA=(6\times 7^2)+(\pi \times (3.5{)}^2)$

$=6\times 49+(\pi \times 12.25)$

$\Rightarrow TSA=332.465c{m}^2$