Question

A hemispherical depression is cut out from one face of a cuboidal block such that the diameter $l\left(\text{cm}\right)$ of the hemisphere is equal to the edge of the cube. Find the surface area of the remaining solid.

Answer 1

Surface area of solid=area of cube + curved surface area of hemisphere -base area of hemisphere

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

$=6l^2+2\pi {\left(\frac{l}{2}\right)}^2-\pi {\left(\frac{l}{2}\right)}^2$

$=6l^2+\pi \frac{l^2}{2}-\pi \frac{l^2}{4}$

$=6l^2+\pi \frac{l^2}{4}$

$=l^2(6+\frac{\pi }{4})$

$=\frac{1}{4}{l}^2(\pi +24)$