From a right cone of height h and with base radius r a cone has been cut of from the centre of the height. The volume of remaining frustum of the cone is.

A cylindrical well of depth 21 m with internal radius of 13 m is dug up. The mud, so detained, is spread evenly to form a platform of dimension 52 × 13.2. What is the height of the platform?

If the areas of circular ring having inner and outer radius 8 cm and 12 cm respectively is equal to the total surface area of cylinder of radius R₁ and height h, then h in terms of R₁ will be :

A regular hexagon has a side of 4 cm. Find its area. (in sq. cm)

The ratio between the length and breadth of a rectangular park is 3: 2. If a man cycling along the boundary of the park at the speed of 12 Km./hr. completes one round in 8 min, then the area of the park in sq.m is – 

A rectangular grass plot 80 m × 60 m has two roads, each 10 m wide, running in the middle of it; one parallel to length and the other parallel to breadth. Find the cost of gravelling the roads at ₹ 2 per m². 

The lengths of the parallel sides of a trapezium are 51 cm and 21 cm, and that of each of the other two sides is 39 cm. what is the area ( in cm²) of the trapezium?

50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is $$ {4 m^{3}}$$ , then the rise in the water level in the tank will be: