What is the difference between the perimeters of two circles of radius 7 cm and 14 cm respectively?

Solution:

Using the formula of the circumference of circle C = 2πr, we find the radius of the circle.

Radius (r₁) of the 1st circle = 19 cm

Radius (r₂) of the 2nd circle = 9 cm

Let the radius of the 3rd circle be r.

Circumference of the 1st circle = 2πr₁ = 2π (19) = 38π

Circumference of the 2nd circle = 2πr₂ = 2π (9) = 18π

Circumference of the 3rd circle = 2πr

Given that,

Circumference of the 3rd circle = Circumference of the 1st circle + Circumference of the 2nd circle

2πr = 38π + 18π

2πr = 56π

r = 56π/2π

r = 28

Therefore, the radius of the circle that has a circumference equal to the sum of the circumference of the two given circles is 28 cm.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 12

Video Solution:

The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.

NCERT Solutions Class 10 Maths Chapter 12 Exercise 12.1 Question 1

Summary:

If the radius of two circles are 19 cm and 9 cm respectively, the radius of the circle which has a circumference equal to the sum of the circumferences of the two circles is 28 cm.

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Solution:

We use the concepts related to areas of sectors of circles and concentric circles.

In a circle with radius r and the angle at the centre with degree measure θ,

Area of the sector = θ/360° × πr2

The area of the shaded region can be calculated by subtracting the area of the sector of the smaller circle from the area of the sector of the larger circle.

Area of shaded region ABDC = Area of sector ACO - Area of sector BDO

Radius of the larger circle, R = OA = 14cm

Radius of the smaller circle, r = OB = 7cm

The angle at the centre, θ = 40°

Area of shaded region ABDC = Area of sector ACO - Area of sector BDO

= θ/360° × πR2 - θ/360° × πr2

= θ/360° π (R2 - r2)

= θ/360° π (R + r )(R - r)

= 40°/360° × 22/7 × (14 + 7) (14 - 7)

= 1/9 × 22/7 × 21 × 7

= (22 × 21 × 7)/(9 × 7)

= (22 × 7)/3

= 154/3 cm2

☛ Check: NCERT Solutions for Class 10 Maths Chapter 12

Video Solution:

Find the area of the shaded region in Fig. 12.20, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and ∠ AOC = 40°.

NCERT Solutions Class 10 Maths Chapter 12 Exercise 12.3 Question 2

Summary:

The area of the shaded region in the figure if the radii of the two concentric circles with center O are 7 cm and 14 cm respectively and ∠AOC = 40° is 154/3 cm2.

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