Question

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

Answer 1

$greatest \: diameter \: = 7cm$
$area \: of \: solid = 6 {a }^{2} - \pi {r}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + 2\pi {r}^{2}$
$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 6 {a }^{2} + \pi {r}^{2}$
$= 6 \times 7 \times 7 + 22 \div 7 \times 3.5 \times 3.5$
$332.5 {cm}^{2}$