Angles and Arc Lengths OP Malhotra S.Chand ISC Class-11 Maths Solutions

Angles and Arc Lengths OP Malhotra S.Chand ISC Class-11 Maths Solutions Chapter-3. Step by step Solutions of OP Malhotra S.Chand ISC Class-11 Mathematics with Exe-3 with Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

Angles and Arc Lengths OP Malhotra S.Chand ISC Class-11 Maths Solutions

Class: 11th
Subject: Mathematics
Chapter  : Ch-3 Angles and Arc Lengths of Section -A
Board ISC
Writer  OP Malhotra
Publications S.Chand Publications 2020-21

-: Select Topics :- 

Exe-3

Chapter Test


Angles and Arc Lengths OP Malhotra S.Chand ISC Class-11 Maths Solutions

Arc Length Formula

The angle that is created by the arc at the middle of the circle is nothing but the angle measure. It’s described by the letter m preceding the name. For instance, mABˆ = 600is read as “the arc AB has a measure of 60 degrees”.

Therefore, the arc length formula is given by:

When the central angle is measured in degrees, the arc length formula is:

Arc length = 2πr(θ/360)

where,

θ indicates the central angle of the arc in degrees

r indicates the radius of the arc

When the central angle is in radians, the arc length formula is:

Arc length = r. θ

Where,

θ indicates the central angle of the arc in radians.

r indicates the radius of the arc.

 Arc and Arc Length:

An arc is any connected part of the circumference of the given circle. An arc length is a distance from one endpoint of the arc to the other. Thus to find an arc length we will require the knowledge a bit about the geometry of a circle.

Since the arc is a portion of the circumference of the circle and we also know that complete circumference is making 360 degrees angle at the center of the circle. So, by knowing the portion of the circumference i.e. arc and arc’s central angle we can easily find the length of the arc.

An angle is a geometrical figure when two lines meet at a common point on a plane. In a given circle, the length of the arc is a portion of the length of its circumference. The arc length will be the measure of the distance along the curved line making up the arc. It will be longer than the straight line distance between its endpoints which is known as a chord.


Exe-3

Angles and Arc Lengths OP Malhotra S.Chand ISC Class-11 Maths Solutions

(Page 3-8)

Question 1-

Express the following angles in degree :

π/6, (14/15)π, (11/18)π, 7/90π.

Question 2-

……………………

………………….

……………………

Question 4-

The perimeter of a certain sector of a circle is equal to the length of the arc of the semi-circle having the same radius, express the angle of the sectors in degree, minutes and seconds

Question 5-

……………………….

Question 6-

The minute hand of a clock is 15 cm long. How far does the tip of the hand move during 40 minute ?

Question 7-

………………………..

Question 8-

The moon’s distance from the earth is 360000 km and diameter subtends an angle of 31′ at the eye of the observe. Find the diameter of the moon.

Question 9-

……………………..

……………………..

Question 12-

Find the area of sectors of a circle radius 5 m bounded by an arc of length 8 m.

Question 15-

What is the ratio of the areas of the major sector in diagram A to the minor sectors in diagram B?


Chapter Test

Angles and Arc Lengths OP Malhotra S.Chand ISC Class-11 Maths Solutions

Page 3-10

Question 1-

Find the radian measure of 

(i)…..

(ii)…….

Question 2-

……………….

…………………

Question  6

If in two circle, …………………………. their radii.

Question 7-

In a circle ……………….. arch of the chord.

Question 10-

A horse is tied ……………….. find the length of the rope.

-: End of Angles and Arc Lengths Solution :-

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