ICSE ICSE Class 8 - CISCE Question Bank Solutions for Mathematics

PQRS is a parallelogram whose diagonals intersect at M.
If ∠PMS = 54°, ∠QSR = 25° and ∠SQR = 30° ; find :

(i) ∠RPS
(ii) ∠PRS
(iii) ∠PSR.

Given: Parallelogram ABCD in which diagonals AC and BD intersect at M.
Prove: M is the mid-point of LN.

ABCD is a parallelogram. What kind of quadrilateral is it if : AC = BD and AC is perpendicular to BD?

ABCD is a parallelogram. What kind of quadrilateral is it if: AC is perpendicular to BD but is not equal to it?

ABCD is a parallelogram. What kind of quadrilateral is it if: AC = BD but AC is not perpendicular to BD?

Prove that the diagonals of a parallelogram bisect each other.

In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.

In parallelogram ABCD, E is the mid-point of side AB and CE bisects angle BCD. Prove that:

1. AE = AD,
2. DE bisects and ∠ADC and
3. Angle DEC is a right angle.

In the following diagram, the bisectors of interior angles of the parallelogram PQRS enclose a quadrilateral ABCD.

Show that:
(i) ∠PSB + ∠SPB = 90°
(ii) ∠PBS = 90°
(iii) ∠ABC = 90°
(iv) ∠ADC = 90°
(v) ∠A = 90°
(vi) ABCD is a rectangle
Thus, the bisectors of the angles of a parallelogram enclose a rectangle.

In parallelogram ABCD, X and Y are midpoints of opposite sides AB and DC respectively. Prove that:

(i) AX = YC
(ii) AX is parallel to YC
(iii) AXCY is a parallelogram.

The given figure shows parallelogram ABCD. Points M and N lie in diagonal BD such that DM = BN.

Prove that:
(i) ∆DMC = ∆BNA and so CM = AN
(ii) ∆AMD = ∆CNB and so AM CN
(iii) ANCM is a parallelogram.

Use the information given in the alongside diagram to find the value of x, y, and z.

In the given figure, AB || EC, AB = AC and AE bisects ∠DAC. Prove that:

1. ∠EAC = ∠ACB
2. ABCE is a parallelogram.

A cube of edge 6 cm and a cuboid with dimensions 4 cm x x cm x 15 cm are equal in volume. Find:
(i) the value of x.
(ii) the total surface area of the cuboid.
(iii) the total surface area of the cube.
(iv) which of these two has a greater surface and by how much?

The height of a rectangular solid is 5 times its width and its length is 8 times its height. If the volume of the wall is 102.4 cm³, find its length.

The length, breadth, and height of a cuboid (rectangular solid) are 4 : 3: 2.
(i) If its surface area is 2548 cm², find its volume.
(ii) If its volume is 3000 m³, find its surface area.

The height of a circular cylinder is 20 cm and the diameter of its base is 14 cm. Find:
(i) the volume
(ii) the total surface area.

Find the curved surface area and the total surface area of a right circular cylinder whose height is 15 cm and the diameter of the cross-section is 14 cm.

Find the height of the cylinder whose radius is 7 cm and the total surface area is 1100 cm².

The curved surface area of a cylinder of height 14 cm is 88 cm². Find the diameter of the base of the cylinder.