# Class 10 RD Sharma Solutions – Chapter 15 Areas Related to Circles – Exercise 15.1 | Set 1

**Question 1. Find the circumference and area of a circle of radius of 4.2 cm. **

**Solution:**

Radius = 4.2 cm

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free classeswhich will definitely help them in making a wise career choice in the future.Circumference of a circle = 2πr

= 2 × (22/7) × 4.2

= 26.4 cm

Area of a circle = πr

^{2}= (22/7) x 4.2

^{2}= (22/7) × 4.2 × 4.2

= 55.44 cm

^{2}Therefore, circumference = 26.4 cm and area of the circle = 55.44 cm

^{2}

**Question 2. Find the circumference of a circle whose area is 301.84 cm**^{2}.

^{2}.

**Solution:**

Area of circle = 301.84 cm

^{2 }Area of a Circle = πr

^{2 }= 301.84 cm^{2 }(22/7) × r

^{2}= 301.84r

^{2}= 96.04r = √96.04 = 9.8cm

Radius = 9.8 cm.

Circumference of a circle = 2πr

= 2 × (22/7) × 9.8

= 61.6 cm

Therefore, the circumference of the circle = 61.6 cm.

**Question 3. Find the area of a circle whose circumference is 44 cm.**

**Solution:**

Circumference = 44 cm

2πr = 44 cm

2 × (22/7) × r = 44

r = 7 cm

Area of a Circle = πr

^{2}= (22/7) × 7 × 7

= 154 cm

^{2}Therefore, area of the Circle = 154 cm

^{2}

**Question 4. 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

Diameter (d) = 2r

Circumference of a circle (C) = 2πr

C = d + 16.8

2πr = 2r + 16.8

2πr – 2r = 16.8

2r (π – 1) = 16.8

2r (3.14 – 1) = 16.8

r = 3.92 cm

Radius = 3.92 cm

Circumference (C) = 2πr

C = 2 × 3.14 × 3.92

= 24.62 cm

Therefore, circumference of the circle = 24.64 cm.

**Question 5. A horse is tied to a pole with 28 m long string. Find the area where the horse can graze.**

**Solution:**

Length of the string = 28 m

Area the horse can graze is the area of the circle with a radius equal to the length of the string.

Area of a Circle = πr

^{2}= (22/7) × 28 × 28

= 2464 m

^{2}Therefore, the area where horse can graze = 2464 m

^{2}

**Question 6. A steel wire when bent in the form of a square encloses an area of 121 cm**^{2}. If the same wire is bent in the form of a circle, find the area of the circle.

^{2}. If the same wire is bent in the form of a circle, find the area of the circle.

**Solution:**

Area of the square = a

^{2}= 121 cm

^{2}Area of the circle = πr

^{2}121 cm

^{2}= a^{2}Therefore, a = 11 cm

Perimeter of square = 4a

= 4 × 11 = 44 cm

Perimeter of the square = Circumference of the circle

Circumference = 2πr

44 = 2(22/7)r

r = 7 cm

Area of the Circle = πr

^{2}= (22/7) × 7 × 7

= 154 cm

^{2}Therefore, the area of the circle = 154 cm

^{2}.

**Question 7. The circumference of two circles are in the ratio of 2:3. Find the ratio of their areas.**

**Solution:**

Circumference of a circle (C) = 2πr

Circumference of first circle = 2πr

_{1}Circumference of second circle = 2πr

_{2}.2πr

_{1}: 2πr_{2 }= 2:3Therefore,

r

_{1}: r_{2}= 2: 3Area of circle 1 = (πr

_{1})^{2}Area of circle 2 = (πr

_{2})^{2}Ratio = 2

^{2}:3^{2}= 4/9

Therefore, ratio of areas = 4: 9.

**Question 8. 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:**

Sum of radii of two circles i.e., r

_{1}+ r_{2}= 140 cm … (i)Difference of their circumference,

C

_{1}– C_{2}= 88 cm2πr

_{1}– 2πr_{2 }= 88 cm2(22/7)(r

_{1}– r_{2}) = 88 cm(r

_{1}– r_{2)}= 14 cmr

_{1 =}r_{2}+ 14…..(ii)From (i) and (ii)

r

_{2 }+ r_{2}+ 14 = 1402r

_{2}= 140 – 142r

_{2 }= 126r

_{2}= 63 cmr

_{1 }= 63 + 14 = 77 cmTherefore,

Diameter of circle 1

_{ }= 2 x 77 = 154 cmDiameter of circle 2

_{ }= 2 × 63 = 126 cm

**Question 9. 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:**

Radius of circle 1 = r

_{1}= 15 cmRadius of circle 2 = r

_{2}= 18 cmC

_{1}= 2πr_{1 ,}C_{2}= 2πr_{2}C = C

_{1}+ C_{2}2πr = 2πr

_{1}+ 2πr_{2}r = r

_{1}+ r_{2 }r = 15 + 18

r = 33 cm

Therefore, the radius of the circle = 33 cm

**Question 10. The radii of 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:**

Radii of the two circles are 6 cm and 8 cm

Area of circle with radius 8 cm = π (8)

^{2}= 64π cm

^{2}Area of circle with radius 6cm = π (6)

^{2}= 36π cm

^{2}Sum of areas = 64π + 36π = 100π cm

^{2}Let the radius of the circle be r cm

Area of the circle = 100π cm

^{2}πr

^{2 }= 100πr= √100 = 10 cm

Therefore, the radius of the circle = 10 cm.