**Selina Concise Class 9 Maths Chapter 20 ****Area and Perimeter Of A Plane Figures**** Exercise 20C Solutions**

**EXERCISE – 20C**

**(1) The diameter of a circle is 28 cm. **

**Find it’s (i) Circumference**

**(ii) Area**

**Solution:**

Given:

Diameter = 28cm.

**∴ **radius = diameter/2

= 28/2

(r) radius = 14 Cm.

(i) Circumference = 2 π r.

= 2 × 22/7 × 14

= 2 × 22 × 2

= 88

(ii) Area of Circle = π r^{2}

= 22/7 × (14)^{2}

= 22/7 × 14 × 14

= 22 × 14 × 2

= 44 × 14

= 616 Cm^{2}.

**(2) The Circumference of a Circular field is 308 m. Find is:**

**(i) Radius **

**(ii) Area.**

**Solution:**

Given: Circumference = 308 m

2 π r = 308

r = 308/2 π

r = 308/2 × 22/7

r = 154 × 7/ 22

r = 7 × 7

r = 49 m

Area of circle = πr^{2}

= 22/7 × (49)^{2}

= 22/7 × 49 × 49

Area of circle = 22 × 49 × 7

= 7. 546 cm^{2}

** **

**(3) The Sum of the circumference and diameter of a circle is 116 cm. Find it’s radius.**

**Solution:**

Given:

The Sum of the circumference and diameter of a circle is 116 cm.

C + d = 116 cm

2 π r + 2r = 116

2r (π + 1) = 116

r (π + 1) = 116/2

r (π + 1) = 58

r = 58/ π + 1

r = 58/22/7 + 1

r = 58/22/7 + 7

r = 58 × 7/ 29

r = 2 × 7

r = 14 cm

**(4) The radii of two circles are 25 cm and 18 cm. Find the radius of the circle which has circumference equal to the sum of circumferences of these two circles.**

**Solution:**

Let r_{1} = 25 cm

R_{2} = 18 cm

Circumference = C_{1} + C_{2}

2 π r = 2 π r_{1} + 2 π r_{2}

2 π r = 2 π ( r_{1} + r_{2})

2 π r = r_{1} + r_{2}

r = r_{1} + r_{2}

r = 25 + 18

r = 43 cm

**∴ **The radius of the circle is 43 cm.

**(5) The radii of two ****circle ****48 cm and 13 cm find the area of the circle which has it’s circumference equal to the difference of the circumferences of the given two circles.**

**Solution:**

Circumference = C_{1} – C_{2}

The Circumference equal to the difference of the circumferences of the given two circles.

**∴ **circumference = C_{1} – C_{2}

2 π r = 2 π r_{1} – 2 π r_{2}

2 π r = 2 π ( r_{1} – r_{2})

r = r_{1} – r_{2}

r = 48 – 13

r = 35 cm

Area of circle = πr^{2}

= 22/7 × (35)^{2}

= 22/7 × 35 × 35

= 22 × 35 × 5

= 110 × 35

= 3850 cm^{2}

**∴ **The area of circle is 3850 Cm^{2}.

**Here is your solution of Selina Concise Class 9 Maths Chapter 20 Area and Perimeter Of A Plane Figures Exercise 20C**

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