English Medium कक्षा ९ - CBSE Question Bank Solutions

Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that ar (APB) × ar (CPD) = ar (APD) × ar (BPC).

[Hint : From A and C, draw perpendiculars to BD.]

P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP, show that

(i) ar(PRQ) = 1/2 ar(ARC)

(ii) ar(RQC) = 3/8 ar(ABC)

(iii) ar(PBQ) = ar(ARC)

In the following figure, ABC is a right triangle right angled at A. BCED, ACFG and ABMN are squares on the sides BC, CA and AB respectively. Line segment AX ⊥ DE meets BC at Y. Show that:-

(i) ΔMBC ≅ ΔABD

(ii) ar (BYXD) = 2 ar(MBC)

(iii) ar (BYXD) = ar(ABMN)

(iv) ΔFCB ≅ ΔACE

(v) ar(CYXE) = 2 ar(FCB)

(vi) ar (CYXE) = ar(ACFG)

(vii) ar (BCED) = ar(ABMN) + ar(ACFG)

Note : Result (vii) is the famous Theorem of Pythagoras. You shall learn a simpler proof of this theorem in Class X.

Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?

Suppose you are given a circle. Give a construction to find its centre.

If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.

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]`

Find the radius of a sphere whose surface area is 154 cm².

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

The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface area.

A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.

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

A right circular cylinder just encloses a sphere of radius r (see figure). Find

1. surface area of the sphere,
2. curved surface area of the cylinder,
3. ratio of the areas obtained in (i) and (ii).

A survey conducted by an organisation for the cause of illness and death among the women between the ages 15 - 44 (in years) worldwide, found the following figures (in %):-

1. Represent the information given above graphically.
2. Which condition is the major cause of women’s ill health and death worldwide?
3. Try to find out, with the help of your teacher, any two factors which play a major role in the cause in (ii) above being the major cause.