RD Sharma Solutions for Class 10 Maths Chapter 15 Areas Related to Circles

RD Sharma Solutions for Class 10 Maths Chapter 15 – Areas Related to Circles provide a comprehensive resource to help students strengthen their understanding and boost their performance in board exams. This chapter holds significant importance as circles and circular shapes are commonly encountered in various real-life situations, making the concepts both practical and essential.

Chapter 15 focuses on calculating the areas of sectors and segments—two special parts of a circular region. The RD Sharma Solutions offer detailed, step-by-step explanations that simplify complex problems, allowing students to grasp core mathematical concepts effectively and apply them confidently in exams.

Designed to reinforce conceptual clarity, these solutions guide students through multiple problem-solving techniques, improving both accuracy and speed. With clear and descriptive answers, RD Sharma Class 10 Maths Solutions serve as an ideal study tool for mastering the chapter on Areas Related to Circles and preparing efficiently for the Class 10 board examination.

Download RD Sharma Solutions for Class 10 Maths Chapter 15 Areas Related to Circles Here

Access the RD Sharma Solutions for Class 10 Maths Chapter 15 – Areas Related to Circles

Q. Find the circumference of a circle whose area is 301.84 cm². 

Solution:

Given,

Area of the circle = 301.84 cm²

We know that

Area of a Circle = πr² = 301.84 cm²

(22/7) × r² = 301.84

r² = 13.72 x 7 = 96.04

r = √96.04 = 9.8

So, the radius is = 9.8 cm.

Now, the circumference of a circle = 2πr

= 2 × (22/7) × 9.8 = 61.6 cm

Hence, the circumference of the circle is 61.6 cm.

Q. The circumference of a circle exceeds the diameter by 16.8 cm. Find the circumference of the circle.

Solution:

Let the radius of the circle be r cm.

So, the diameter (d) = 2r [As radius is half the diameter]

We know that,

Circumference of a circle (C) = 2πr

From the question,

The circumference of the circle exceeds its diameter by 16.8 cm.

C = d + 16.8

2πr = 2r + 16.8 [d = 2r]

2πr – 2r = 16.8

2r (π – 1) = 16.8

2r (3.14 – 1) = 16.8

r = 3.92 cm

Thus, radius = 3.92 cm

Now, the circumference of the circle (C) = 2πr

C = 2 × 3.14 × 3.92

= 24.64 cm

Q. Find the circumference and area of a circle of radius of 4.2 cm. 

Solution: Given,

Radius (r) = 4.2 cm

We know that

Circumference of a circle = 2πr

= 2 × (22/7) × 4.2 = 26.4 cm²

Area of a circle = πr²

= (22/7) x 4.2²

= 22 x 0.6 x 4.2 = 55.44 cm²

Q. The sum of the radii of two circles is 140 cm, and the difference of their circumference is 88 cm. Find the diameters of the circles. 

Solution:

Let the radii of the two circles be r₁ and r₂.

And the circumferences of the two circles be C₁ and C₂.

We know that the circumference of the circle (C) = 2πr

Given,

Sum of radii of two circle, i.e., r₁ + r₂ = 140 cm … (i)

Difference of their circumference,

C₁ – C₂ = 88 cm

2πr₁ – 2πr₂ = 88 cm

2(22/7)(r₁ – r₂) = 88 cm

(r₁ – r₂₎ = 14 cm

r_{1 =} r₂ + 14…..(ii)

Substituting the value of r₁ in equation (i), we have

r₂ + r₂ + 14 = 140

2r₂ = 140 – 14

2r₂ = 126

r₂ = 63 cm

Substituting the value of r₂ in equation (ii), we have

r₁ = 63 + 14 = 77 cm

Therefore,

Diameter of circle 1 = 2r₁ = 2 x 77 = 154 cm

Diameter of circle 2 = 2r₂ = 2 × 63 = 126 cm

Q.The radii of the two circles are 8 cm and 6 cm, respectively. Find the radius of the circle having its area equal to the sum of the areas of two circles.

Solution: Given,

The Radii of the two circles are 6 cm and 8 cm.

The area of circle with radius 8 cm = π (8)² = 64π cm²

The area of circle with radius 6cm = π (6)² = 36π cm²

The sum of areas = 64π + 36π = 100π cm²

Let the radius of the circle be x cm.

Area of the circle = 100π cm² (from above)

πx² = 100π

x = √100 = 10 cm

Q. Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii 15cm and 18cm.

Solution:

Given,

Radius of circle 1 = r₁ = 15 cm

Radius of circle 2 = r₂ = 18 cm

We know that the circumference of a circle (C) = 2πr

So, C₁ = 2πr₁ and C₂ = 2πr₂

Let the radius be r of the circle which is to be found and its circumference (C).

Now, from the question,

C = C₁ + C₂

2πr = 2πr₁ + 2πr₂

r = r₁ + r₂ [After dividing by 2π both sides]

r = 15 + 18

r = 33 cm

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

Solution: Given,

Radius of circle 1 = r₁ = 19 cm

Radius of circle 2 = r₂ = 9 cm

We know that the circumference of a circle (C) = 2πr

So, C₁ = 2πr₁ and C₂ = 2πr₂

Let the radius be r of the circle which is to be found and its circumference (C).

Now, from the question,

C = C₁ + C₂

2πr = 2πr₁ + 2πr₂

r = r₁ + r₂ [After dividing by 2π both sides]

r = 19 + 9

r = 28 cm

Thus, the radius of the circle = 28 cm

So, the area of required circle = πr² = (22/7) × 28 × 28 = 2464 cm²