## NCERT Solutions for Class 10 Maths Exercise 12.1 Chapter 12 Area Related to Circles- FREE PDF Download

NCERT Class 10 Maths Ch 12 is one of the most important ones in the NCERT syllabus. Duly following NCERT Solutions for Class 10 Maths

Chapter 12 ensures you that there will be no hindrance when you opt for more advanced branches of Maths. This is where CoolGyan comes in. Our free Class 10 Area Related to Circles solutions will help you understand the chapter thoroughly.

# NCERT Solutions for Class 10 Maths Chapter 12 – Area Related to Circles

Unless stated otherwise, take π=227π=227

1. 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.

**Ans.**Let R be the radius of the circle which has circumference equal to the sum of circumferences of the two circles, then according to question,

⇒⇒ 2πR=2π(19+9)2πR=2π(19+9)

R = 19 + 9

R = 28 cm

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

**Ans.**Let R be the radius of the circle which has area equal to the sum of areas of the two circles, then

According to the question,

⇒⇒ πR2=π[(8)2+(6)2]πR2=π[(8)2+(6)2]

R^{2} = 64 + 36

R^{2} = 100

R = 10 cm

3. Figure depicts an archery target marked with its five scoring areas from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of the five scoring regions.

**Ans.**Gold: Diameter = 21 cm

Radius = cm

Area of gold scoring region =

= = 346.5 cm^{2}

Red: Area of red scoring region =

=

= 227×21×21−346.5227×21×21−346.5

= 1386 – 346.5 =

Blue: Area of blue scoring region = π(21+10.5)2−(1039.5+346.5)π(21+10.5)2−(1039.5+346.5)

=

=

= 3118.5 – 1386 =

Black: Area of black scoring region =

=

=

= 5544 – 3118.5 =

White: Area of white scoring region =

=

=

= 8662.5 – 5544 =

4. The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?

**Ans.**Diameter of wheel = 80 cm

Radius of wheel = 40 cm

Distance covered by wheel in one revolution = = = cm

Distance covered by wheel in 1 hour = 66 km = 66000 m = 6600000 cm

Distance covered by wheel in 10 minutes = = 1100000 cm

No. of revolutions =

= = 4375

5. Tick the correct answer in the following and justify your choice: If the perimeter and area of a circle are numerically equal, then the radius of the circle is:

(A) 2 units

(B) units

(C) 4 units

(D) 7 units

**Ans.**(A)

Circumference of circle = Area of circle

= 2 units