To comfortably sit in a room, every girl must be allowed a floor space of 2 sq.m. and air space of 5.5 cubic metres.  Fifty girls are to be seated comfortably in a room 10m. long.  What should be its height?

A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by

If an arc of 60⁰ on circle I has the same length as an arc of 45⁰ on circle II, what is the ratio of thearea of circle I to that of circle II ?

There are 8436 steel balls, each with a radius of 1 centimeter, stacked in a pile, with 1 ball on top, 3 balls in the second layer, 6 in the third layer, 10 in the fourth, and so on. The number of horizontal layers in the pile is

The length of a ladder is exactly equal to the height of the wall it is resting against. Iflower end of the ladder is kept on a stool of height 3 m and the stool is kept 9 m awayfrom the wall, the upper end of the ladder coincides with the top of the wall. Then,the height of the wall is:

A rectangular tank measuring 5m x 4.5 m x 2.1 m is dug in the centre of the field measuring 13.5.m x 2.5. The earth dug out is spread evenly over the remaining portion of afield. How much is the level of the field raised ?