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A room is in the form of cylinder surmounted by a hemi-spherical dome. The base radius of hemisphere is one-half the height of cylindrical part. Find total height of the room if it contains $\frac{1408}{21}$ m$^3$ of air. Take $\pi = \frac{22}{7}$
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Let $h$ be height of cylindrical part and $r$ be radius of hemisphere
Volume of room = $2\pi r^3 + \frac{2}{3} \pi r^3 = \frac{1408}{21}$
$\Rightarrow r=2$
Therefore, $h=4$
Height of the room is = $6$m
Volume of room = $2\pi r^3 + \frac{2}{3} \pi r^3 = \frac{1408}{21}$
$\Rightarrow r=2$
Therefore, $h=4$
Height of the room is = $6$m