The square on the diagonal of a cube has an area of 1875 cm². Calculate :

(i) the side of the cube,

(ii) the surface area of the cube.

The areas of three adjacent faces of a cuboid are x, y and z sq. units. If the volume is V cubic units, prove that V² = xyz.

Water flows into a tank 150 m long and 100 m broad through a rectangular pipe whose cross section is 5 dm × 3.5 dm, at the speed of 15 km/hr. In what time, will the water be 7 m deep?

A rectangular tank is 25 m long and 7.5 m deep. If 540 m³ of water be drawn off the tank, the level of water in the tank goes down by 1.8 m. Calculate :

(i) the width of the tank

(ii) the capacity of the tank.