English Medium Class 9 - CBSE Question Bank Solutions for Mathematics

If a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of the cone is

A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder. If the radius of the sphere is r, then the volume of the cylinder is 

The ratio between the volume of a sphere and volume of a circumscribing right circular cylinder is 

A cone and a hemisphere have equal bases and equal volumes the ratio of their heights is

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is

Opposite angles of a quadrilateral ABCD are equal. If AB = 4 cm, determine CD.

The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is ______.

The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠DAC = 32º and ∠AOB = 70º, then ∠DBC is equal to ______.

Diagonals AC and BD of a parallelogram ABCD intersect each other at O. If OA = 3 cm and OD = 2 cm, determine the lengths of AC and BD.

Diagonals of a parallelogram are perpendicular to each other. Is this statement true? Give reason for your answer.

Diagonals of a quadrilateral ABCD bisect each other. If ∠A = 35º, determine ∠B.

E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram.

Points P and Q have been taken on opposite sides AB and CD, respectively of a parallelogram ABCD such that AP = CQ (Figure). Show that AC and PQ bisect each other.

In a parallelogram ABCD, AB = 10 cm and AD = 6 cm. The bisector of ∠A meets DC in E. AE and BC produced meet at F. Find the length of CF.

A diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus.

In the following figure, AB || DE, AB = DE, AC || DF and AC = DF. Prove that BC || EF and BC = EF.

P and Q are points on opposite sides AD and BC of a parallelogram ABCD such that PQ passes through the point of intersection O of its diagonals AC and BD. Show that PQ is bisected at O.

ABCD is a rectangle in which diagonal BD bisects ∠B. Show that ABCD is a square.

P is the mid-point of the side CD of a parallelogram ABCD. A line through C parallel to PA intersects AB at Q and DA produced at R. Prove that DA = AR and CQ = QR.

ABCD is a rhombus in which altitude from D to side AB bisects AB. Find the angles of the rhombus.