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

A square is inscribed in a circle of radius 7 cm. Find the area of the square.

The given figures show a rectangle ABCD inscribed in a circle as shown alongside.
If AB = 28 cm and BC = 21 cm, find the area of the shaded portion of the given figure.

Two circles touch each other externally. The sum of their areas is 58π cm² and the distance between their centers is 10 cm. Find the radii of the two circles.

The diameters of two circles are 32 cm and 24 cm. Find the radius of the circle having its area equal to the sum of the areas of the two given circles.

The minute hand of a clock is 8 cm long. Find the area swept by the minute hand between 8.30 a.m. and 9.05 a.m.

A circle of the largest area is cut from a rectangular piece of cardboard with dimensions 55 cm and 42 cm. Find the ratio between the area of the circle cut and the area of the remaining card-board.

The following figure shows a square cardboard ABCD of side 28 cm. Four identical circles of the largest possible sizes are cut from this card as shown below.

Find the area of the remaining card-board.

The radii of two circles are in the ratio 3: 8. If the difference between their areas is 2695π cm², find the area of the smaller circle. 

The diameters of three circles are in the ratio 3: 5: 6. If the sum of the circumferences of these circles is 308 cm; find the difference between the areas of the largest and the smallest of these circles.

Find the area of a ring-shaped region enclosed between two concentric circles of radii 20 cm and 15 cm.

If a square in inscribed in a circle, find the ratio of the areas of the circle and the square.

Two circles touch each other externally. The sum of their areas is 74π cm² and the distance between their centers is 12 cm. Find the diameters of the circle.

A steel wire, when bent in the form of a square, encloses an area of 121 cm². The same wire is bent in the form of a circle. Find area the circle. 

Two circles touch externally. The sum of their areas is 130π sq. cm and the distance between their centers is 14 cm. Find the radii of the circles.

A hose-pipe of cross-section area 2 cm² delivers 1500 liters of water in 5 minutes. What is the speed of water in m/s through the pipe? 

Water is discharged from a pipe of a cross-section area 3.2 cm² at the speed of 5m/s. Calculate the volume of water discharged: 
(i) In cm³ per sec.
(ii) In liters per minute.

A rectangular tank 30 cm × 20 cm × 12 cm contains water to a depth of 6 cm. A metal cube of side 10 cm is placed in the tank with its one face resting on the bottom of the tank. Find the volume of water, in liters, that must be poured in the tank so that the metal cube is just submerged in the water. 

Plot the following points on the same graph paper:
(i) (8, 7)
(ii) (3, 6)
(iii) (0, 4)
(iv) (0, -4)
(v) (3, -2)
(vi) (-2, 5)
(vii) (-3, 0)
(viii) (5, 0)
(ix) (-4, -3)

By plotting the following points on the same graph paper. Check whether they are collinear or not:
(i) (3, 5), (1, 1) and (0, -1)
(ii) (-2, -1), (-1, -4) and (-4, 1)

In square ABCD; A = (3, 4), B = (-2, 4) and C = (-2, -1). By plotting these points on a graph paper, find the co-ordinates of vertex D. Also, find the area of the square.