MENU

RD Chapter 15 Areas Related to Circles Ex 15.2 Solutions

Question - 21 : - In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find (0 the length of the arc (ii) area of the secter formed by the arc. (Use π = 22/7) [CBSE 2013]

Answer - 21 : -

Radius of a circle (r) = 21 cm
Angle at the centre = 60°

Question - 22 : - From a circular piece of cardboard of radius 3 cm two sectors of 90° have been cut off. Find the perimeter of the remaining portion nearest hundredth centimeters (Take π = 22/7).

Answer - 22 : -

Radius of the circular piece of cardboard (r) = 3 cm
 
∴ Two sectors of 90° each have been cut off
∴ We get a semicular cardboard piece
∴ Perimeter of arc ACB

Question - 23 : - The area of a sector is one-twelfth that of the complete circle. Find the angle of the sector.

Answer - 23 : - Let r be the radius of the circle and 0 be the central angle of the sector of the circle Then area of circle = πr2

Question - 24 : - AB is a chord of a circle with centre O and radius 4 cm. AB is of length 4 cm. Find the area of the sector of the circle formed by the chord AB.

Answer - 24 : -

Radius of the circle with centre O (r) = 4 cm
Length of chord AB = 4 cm

Question - 25 : -
In a circle of radius 6 cm, a chord of length 10 cm makes an angle of 110° at the centre of the circle. Find 
(i)  the circumference of the circle,
(ii) the area of the circle,
(iii) the length of the arc AB,
(iv) the area of the sector OAB.

Answer - 25 : -

Radius of the circle (r) = 6 cm
Length of chord = 10 cm
and central angle (θ) =110°

Question - 26 : - Figure, shows a sector of a circle, centre O, containing an angle θ°. Prove that :

Answer - 26 : -

Radius of the circle = r
Arc AC subtends ∠θ at the centre of the
circle. OAB is a right triangle
In the right ΔOAB,

Question - 27 : - Figure, shows a sector of a circle of radius r cm containing an angle θ°. The area of the sector is A cm2 and perimeter of the sector is 50 cm. Prove that

Answer - 27 : -

Radius of the sector of the circle = r cm
and angle at the centre = 0
Area of sector OAB = A cm2
and perimeter of sector OAB = 50 cm

Free - Previous Years Question Papers
Any questions? Ask us!
NodeJS Interview Questions Answers
ASP.Net Interview Questions Answers
Interview Questions Answers
×