NCERT Solutions 11th Maths Chapter 11 Areas Related to Circles Exercise 12.1

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Exercise 12.1
1.The radii of the two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has a circumference equal to the sum of the circumferences of the two circles.
Solution:
Radius of the bigger circle = 19 cm
∴ The Circumference of the bigger circle
= 2πr = 2π x 19 = 38π cm
Radius of the smallest circle = 9 cm
∴ The Circumference of the smaller circle
= 2πr = 2π x 9 = 18π cm
Sum of Circumference of these two circle
= 38π + 18π = 56π cm
Let r be the radius of the required circle.
Then, 2πr = 56π ⇒ r =56π/2π =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.
Solution:
Radius of bigger circle = 8 cm
∴ Area of bigger circle = π x (8)2 = 64π cm2
Radius of smaller circle = 6 cm
∴ Area of smaller circle = π x (6)2 = 36π cm2
Sum of areas of two circles = 64π + 36π
= 100π cm2
Let r be the radius of the required circle.
Then πr2 = 100π
⇒ r2 = 100 ⇒ r =√100 = 10 cm.
3.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 traveling at a speed of 66 km per hour?
Solution:
Radius of one wheel of the car = 40 cm
= 0.4 m.
Distance covered by the wheel to complete one revolution – 2πr x 0.4 = 0.8 m.
Let the wheel of the car completest revolutions in 10 minutes at a speed of 66 km/h.
Then distance covered by the wheel in making r complete revolutions in 10 minutes
= (0.8π x n ) m
Also, distance travelled by car in 60 minutes
= (66 x 1000) m
∴ Distance travelled by car in 1 minute (66*1000)/60m ∴ Distance travelled by car in 10 minutes (66*1000*10)/60 m=11000m According to the question, we have: