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A hemispherical depression is scooped out from the top face of a wooden cubical block of side $14\text{ cm}$. If the diameter of the hemisphere is equal to the side of the cube, find the total surface area of the remaining solid. (Use $\pi = \frac{22}{7}$)
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Solution: Radius of hemisphere $= r = \frac{14}{2} = 7\text{ cm}$
Total surface area of the remaining solid $= 6a^2 - \pi r^2 + 2\pi r^2 = 6a^2 + \pi r^2$
$= 6 \times 14 \times 14 + \frac{22}{7} \times 7 \times 7 = 1330\text{ sq. cm}$
Total surface area of the remaining solid $= 6a^2 - \pi r^2 + 2\pi r^2 = 6a^2 + \pi r^2$
$= 6 \times 14 \times 14 + \frac{22}{7} \times 7 \times 7 = 1330\text{ sq. cm}$