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 $\left(\fr

Question

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 $\left(\frac{1408}{21}\right) m^3$ of air. Take $\left(\pi = \frac{22}{7}\right)$

Accepted Answer

Step 1: Let $h$ be height of cylindrical part and $r$ be radius of hemisphere.
Volume of room $= 2\pi r^2 + \frac{2}{3}\pi r^3 = \frac{1408}{21}$
Step 2: $\Rightarrow r = 2$
Step 3: Therefore, $h = 4$
Height of the room is $= 6$ m

Question

Solution