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A cubical block is surmounted by a hemisphere of radius $3.5\text{ cm}$. What is the smallest possible length of the edge of the cube so that the hemisphere can totally lie on the cube ? Find the total surface area of the solid so formed.
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Edge of cube $= a = 3.5 \times 2 = 7\text{ cm}$
Total surface area of solid
$= 6 a^2 + 2\pi r^2 - \pi r^2$
$= 6 a^2 + \pi r^2$
$= 6 \times 7 \times 7 + \frac{22}{7} \times 3.5 \times 3.5$
$= \frac{665}{2}\text{ sq. cm}$ or $332.5\text{ sq. cm}$
Total surface area of solid
$= 6 a^2 + 2\pi r^2 - \pi r^2$
$= 6 a^2 + \pi r^2$
$= 6 \times 7 \times 7 + \frac{22}{7} \times 3.5 \times 3.5$
$= \frac{665}{2}\text{ sq. cm}$ or $332.5\text{ sq. cm}$