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.