Question

a hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. determine the surface area of the remaining solid.

Answer 1

hope this will help you..........

Answer 2

$\large\sf{Diameter=l\:cm}$

$\large\sf{Radius=\frac{l}{2}cm}$

$\small\sf{SA\:of\:remaining\:solid=TSA\:of\:cube+SA\:of\:hemisphere-area\:of\:cylinder}$

= $\large\sf{{6l}^{2} + {2\pi \: r}^{2} - {\pi \: r}^{2} }$

= $\large\sf{{6l}^{2} + {\pi \: r}^{2}}$

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

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

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