**Q)** 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. Fine the total height of the room if it Contains m^{3} of air. Take

**Ans: **Let h be the height of cylindrical part and r be the radius of hemisphere.

Volume of room =

Given that r = or h = 2r

Volume of room =

=

= x

= 8 x 22 r^{3} = 1408

= r^{3} = 8 or r = 2 m

= h = 2 r = 2 x 2 = 4 m

**Therefore, height of the room is 4 m**