English Medium कक्षा ९ - CBSE Question Bank Solutions for Mathematics

Show that in a quadrilateral ABCD, AB + BC + CD + DA > AC + BD

In a triangle ABC, D is the mid-point of side AC such that BD = `1/2` AC. Show that ∠ABC is a right angle.

ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 140º, then ∠BAC is equal to ______.

ABCD is a cyclic quadrilateral such that ∠A = 90°, ∠B = 70°, ∠C = 95° and ∠D = 105°.

If a line is drawn parallel to the base of an isosceles triangle to intersect its equal sides, prove that the quadrilateral so formed is cyclic.

If a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are also equal.

In the following figure, AOB is a diameter of the circle and C, D, E are any three points on the semi-circle. Find the value of ∠ACD + ∠BED.

If non-parallel sides of a trapezium are equal, prove that it is cyclic.

If P, Q and R are the mid-points of the sides BC, CA and AB of a triangle and AD is the perpendicular from A on BC, prove that P, Q, R and D are concyclic.

ABCD is a parallelogram. A circle through A, B is so drawn that it intersects AD at P and BC at Q. Prove that P, Q, C and D are concyclic.

If bisectors of opposite angles of a cyclic quadrilateral ABCD intersect the circle, circumscribing it at the points P and Q, prove that PQ is a diameter of the circle.

Find the surface area of a sphere of radius 10.5 cm.

`["Assume "pi=22/7]`

Find the surface area of a sphere of radius 5.6 cm.

`["Assume "pi=22/7]`

Find the surface area of a sphere of radius 14 cm.

`["Assume "pi=22/7]`

Find the surface area of a sphere of diameter 14 cm.

`["Assume "pi=22/7]`

Find the surface area of a sphere of diameter 21 cm.

`["Assume "pi=22/7]`

Find the surface area of a sphere of diameter 3.5 m.

`["Assume "pi=22/7]`

Find the total surface area of a hemisphere of radius 10 cm. [Use π = 3.14]

The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of ₹ 16 per 100 cm².

`["Assume "pi=22/7]`