A hemispherical depression of diameter 4 cm is cut out from each face of a cubical block of sides 10 cm. Find the surface area of the remaining solid (in cm²). $$\left( {{\text{Use }}\pi = \frac{{22}}{7}} \right)$$

Solution (By Examveda Team)

Side of cubical block = 10 cm
∴ Area of each face of cubical block = 10² = 100 cm²
Radius of Hemisphere = $$\frac{4}{2}$$ = 2 cm
Surface area of hemisphere
$$\eqalign{ & = 2\pi {r^2} \cr & = 2 \times \frac{{22}}{7} \times {2^2}{\text{ c}}{{\text{m}}^2} \cr & = \frac{{176}}{7}{\text{ c}}{{\text{m}}^2} \cr} $$
Total surface area of hemisphere $$ = 6 \times \frac{{176}}{7} = \frac{{1056}}{7}{\text{ c}}{{\text{m}}^2}$$
Remaining surface area of each face of cubical block
$$\eqalign{ & = {10^2} - 2\pi r \cr & = 100 - 2 \times \frac{{22}}{7} \times 2{\text{ c}}{{\text{m}}^2} \cr & = 100 - \frac{{88}}{7}{\text{ c}}{{\text{m}}^2} \cr & = \frac{{612}}{7}{\text{ c}}{{\text{m}}^2} \cr} $$
∴ Total surface area of 6 remaining cubical block $$ = 6 \times \frac{{612}}{7} = \frac{{3672}}{7}{\text{ c}}{{\text{m}}^2}$$
∴ Surface area of remaining solid
$$\eqalign{ & = \left( {\frac{{1056}}{7} + \frac{{3672}}{7}} \right){\text{c}}{{\text{m}}^2} \cr & = \frac{{4728}}{7}{\text{ c}}{{\text{m}}^2} \cr & = 675\frac{3}{7}{\text{ c}}{{\text{m}}^2} \cr} $$