Frequently Asked Questions on Chapter 12 – Areas Related to Circles
The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has a circumference equal to the sum of the circumferences of the two circles?
The radius of the 1st circle = 19 cm (given)
∴ Circumference of the 1st circle = 2π × 19 = 38π cm
The radius of the 2nd circle = 9 cm (given)
∴ Circumference of the circle = 2π × 9 = 18π cm
So,
The sum of the circumference of two circles = 38π + 18π = 56π cm
Now, let the radius of the 3rd circle = R
∴ The circumference of the 3rd circle = 2πR
It is given that sum of the circumference of two circles = circumference of the 3rd circle
Hence, 56π = 2πR
Or, R = 28 cm.
Tick the correct Solution: in the following and justify your choice : If the perimeter and the area of a circle are numerically equal, then the radius of the circle is 2 units,π units,4 units,7 units?
Since the perimeter of the circle = area of the circle,
2πr = π r2
Or, r = 2
So, option (A) is correct i.e. the radius of the circle is 2 units.
Find the area of a quadrant of a circle whose circumference is 22 cm?
Circumference of the circle = 22 cm (given)
It should be noted that a quadrant of a circle is a sector which is making an angle of 90°.
Let the radius of the circle = r
As C = 2πr = 22,
R = 22/2π cm = 7/2 cm
∴ Area of the quadrant = (θ/360°) × π r2
Here, θ = 90°
So, A = (90°/360°)×π r2cm2
= (49/16) πcm2
=77/8cm2=9.6cm2
Tick the correct solution in the following :Area of a sector of angle p (in degrees) of a circle with radius R is p/180 × 2πR, p/180 × π R2,p/360 × 2πR,p/720 × 2πR2?
The area of a sector = (θ/360°) × π r2
Given, θ = p
So, area of sector = p/360 × π R2
Multiplying and dividing by 2 simultaneously,
= p/360 × 2/2 × πR2
= 2p/720 × 2πR2
So, option (D) is correct.
Find the radius of the circle which has a circumference equal to the sum of the circumferences of the two circles. Given the radii of two circles are 19 cm and 9 cm respectively.
The radius of the 1st circle = 19 cm
Circumference of the 1st circle = 2π × 19 = 38π cm
The radius of the 2nd circle = 9 cm
Circumference of the circle = 2π × 9 = 18π cm
So,
The sum of the circumference of two circles = 38π + 18π = 56π cm
Now, let the radius of the 3rd circle = R
The circumference of the 3rd circle = 2πR
It is given that sum of the circumference of two circles = circumference of the 3rd circle
Hence, 56π = 2πR or R = 28 cm.
If the perimeter and the area of a circle are numerically equal, then the radius of the circle is?
We know that the perimeter of the circle = area of the circle,
2πr = πr^2
Or, r = 2
Hence, the radius of the circle is 2 units.
Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.
It is given that the angle of the sector is 60°
We know that the area of sector = (θ/360°)×πr^2
Area of the sector with angle 60° = (60°/360°) × π r^2 cm^2
= 36/6 π cm^2
= 6 × 22/7 cm^2
= 132/7 cm^2
Hence, the area of the sector of the circle is 132/7 cm^2.