50 circular discs, each of radius 7cm and thickness 0.5cm are placed one above the other. Find the total surface area of the solid so formed. Find how much space will be left in a cubical box of side 25cm if the solid formed is placed inside it.

From a point 100 m above a lake the angle of elevation of a stationary helicopter is 30° and the angle of depression of reflection of the helicopter in the lake is 60ᵒ. Find the height of the helicopter above the lake.

A donor agency ensures milk is supplied in containers, which are in the form of a frustum of a cone to be distributed to flood victims in a camp. The height of each frustum is 30 cm and the radii of whose lower and upper circular ends are 20 cm and 40 cm respectively. If this milk is available at the rate of Rs.35 per litre and 880 litres of milk is needed daily for a camp.

(a) Find how many milk containers are needed daily for the camp.

(b) What daily cost will it put on the donor agency?

(c) What value of the donor agency is depicted in this situation?

The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the bigger circle and BD is tangent to the smaller circle touching it at D and intersecting the larger circle at P, on producing. Find the length of AP.

A manufacturer of TV sets produced 600 units in the 3rd year and 700 units in the 7th year. Assuming that, production increases uniformly by a fixed number of units every year. Find

(i) The production in 1^st year.

(ii) The production in 10^th year.

(iii) The total production in 7 years.