(English Medium) ICSE Class 9 - CISCE Question Bank Solutions

The shaded portion of the figure, given alongside, shows two concentric circles. If the circumference of the two circles is 396 cm and 374 cm, find the area of the shaded portion.

An express train is running between two stations with a uniform speed. If the diameter of each wheel of the train is 42 cm and each wheel makes 1200 revolutions per minute, find the speed of the train.

Each wheel of a car is of diameter 80 cm. How many completer revolutions does each wheel make in 10 minutes when the car is traveling at a speed of 66 km per hour?

A wheel has a diameter of 84 cm. Find how many completer revolutions must it make to cover 3.168 km.

There are two circular gardens A and B. The circumference of garden A is 1.760 km and the area of garden B is 25 times the area of garden A. Find the circumference of garden B.

The circumference of a given circular park is 55 m. It is surrounded by a path of uniform width of 3.5 m. Find the area of the path.

The diameters of the front and the rear wheels of a tractor are 63 cm and 1.54 m respectively. The rear wheel is rotating at `24 6/11` revolutions per minute. Find:
(i) the revolutions per minute made by the front wheel.
(ii) the distance traveled bu the tractor in 40 minutes.

The following figure shows a solid of uniform cross-section. Find the volume of the solid. All measurements are in centimeters.
Assume that all angles in the figures are right angles.

The following figure shows a solid of uniform cross-section. Find the volume of the solid. All measurements are in centimeters.

Assume that all angles in the figures are right angles.

A swimming pool is 40 m long and 15 m wide. Its shallow and deep ends are 1.5 m and 3 m deep respectively. If the bottom of the pool slopes uniformly, find the amount of water in liters required to fill the pool.

The following figure shows a closed victory-stand whose dimensions are given in cm.

Find the volume and the surface area of the victory stand. 

A swimming pool is 18 m long and 8 m wide. Its deep and shallow ends are 2 m and 1.2 m respectively. Find the capacity of the pool, assuming that the bottom of the pool slopes uniformly. 

A rectangular cardboard sheet has length 32 cm and breadth 26 cm. Squares each of side 3 cm, are cut from the corners of the sheet and the sides are folded to make a rectangular container. Find the capacity of the container formed.

A rectangular water-tank measuring 80 cm x 60 cm is filled form a pipe of cross-sectional area 1.5 cm², the water emerging at 3.2 m/s. How long does it take to fill the tank?

The cross-section of a piece of metal 4 m in length is shown below. Calculate :


(i) The area of the cross-section;
(ii) The volume of the piece of metal in cubic centimeters.

If 1 cubic centimeter of the metal weighs 6.6 g, calculate the weight of the piece of metal to the nearest kg.

The cross-section of a tunnel perpendicular to its length is a trapezium ABCD as shown in the following figure; also given that:

AM = BN; AB = 7 m; CD = 5 m. The height of the tunnel is 2.4 m. The tunnel is 40 m long. Calculate:

(i) The cost of painting the internal surface of the tunnel (excluding the floor) at the rate of Rs. 5 per m² (sq. meter).

(ii) The cost of paving the floor at the rate of Rs. 18 per m².

A school auditorium is 40 m long, 30 m broad and 12 m high. If each student requires 1.2 m² of the floor area; find the maximum number of students that can be accommodated in this auditorium. Also, find the volume of air available in the auditorium, for each student. 

The internal dimensions of a rectangular box are 12 cm x  `x` cm x 9 cm. If the length of the longest rod that can be placed in this box is 17 cm; find `x`.   

A rectangular field is 112 m long and 62 m broad. A cubical tank of edge 6 m is dug at each of the four corners of the field and the earth so removed is evenly spread on the remaining field. Find the rise in level.  

State, true or false:
The origin is in the first quadrant.