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# A hemispherical depression is cut of one face of a cubical wooden block such the diameter l of the hemisphere is equal to the edge of the cube. Determine th surface area of the remaining solid.

Edge of the cube =$$l$$

Diameter of the hemisphere = $$l$$

$$\Rightarrow$$ Radius of the hemisphere $$= \frac{l}{2}$$

$$\Rightarrow$$ Area of the remaining solid after cutting out the hemispherical depression.

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

$$= \ 6 l^2 \ + \ \pi \ × \ \frac{l^2}{4} \$$
$$= \ \frac{l^2}{4} (24 \ + \ \pi)$$