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). ( Use = 227 )

Answer: Option C

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
$$\begin{array}{rl}& =2\pi r^2\\ & =2\times \frac{22}{7}\times 2^2\text{ c}{\text{m}}^2\\ & =\frac{176}{7}\text{ c}{\text{m}}^2\end{array}$$
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
$$\begin{array}{rl}& =10^2-2\pi r\\ & =100-2\times \frac{22}{7}\times 2\text{ c}{\text{m}}^2\\ & =100-\frac{88}{7}\text{ c}{\text{m}}^2\\ & =\frac{612}{7}\text{ c}{\text{m}}^2\end{array}$$
∴ 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
$$\begin{array}{rl}& =\left(\frac{1056}{7}+\frac{3672}{7}\right)\text{c}{\text{m}}^2\\ & =\frac{4728}{7}\text{ c}{\text{m}}^2\\ & =675\frac{3}{7}\text{ c}{\text{m}}^2\end{array}$$