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From one of the faces of a solid wooden cube of side 14 cm, maximum number of hemispheres of diameter 1.4 cm are scooped out. Find the total number of hemispheres that can be scooped out. Also, find the total surface area of the remaining solid.
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Total number of hemispheres $= \frac{14 \times 14}{1.4 \times 1.4} = 100$
Total Surface Area of remaining solid = Surface Area of Cube + Curved Surface Area of 100 hemispheres - Area of 100 circles
$= 6 \times 14 \times 14 + 100 \times 2 \times \frac{22}{7} \times 0.7 \times 0.7 - 100 \times \frac{22}{7} \times 0.7 \times 0.7$
$= 1330$
$\therefore$ Total surface area of remaining solid is 1330 cm$^2$.
Total Surface Area of remaining solid = Surface Area of Cube + Curved Surface Area of 100 hemispheres - Area of 100 circles
$= 6 \times 14 \times 14 + 100 \times 2 \times \frac{22}{7} \times 0.7 \times 0.7 - 100 \times \frac{22}{7} \times 0.7 \times 0.7$
$= 1330$
$\therefore$ Total surface area of remaining solid is 1330 cm$^2$.