NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles Exercise 12.1

In this page we have NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles for
EXERCISE 12.1 . Hope you like them and do not forget to like , social share
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Question 1) The radii of the two circles are 19cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles. Solution 1:
According to the question
Circumference of Ist circle = 2π(19) =38 π cm
Circumference of 2^{nd} circle = 2π(9) =18 π cm
Let r be the radius of the new circle
Circumference of New circle = 2π(r) =2 πr cm
Now
2πr=38π+18π
Or r =28 cm Question 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 2:
According to the question
Area of Ist circle =πr^{2}=π(64)=64π
Area of 2^{nd} circle =πr^{2}=π(36)=36π
Let r the radius of new circle
Area of New circle=πr^{2}
Now as per question
πr^{2}= 64 π+36 π
r=10cm Question 3. The below depicts an archery target marked with its five scoring regions 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 each of the five scoring regions.

Solution:
Diameter of Gold Circle is given as =21 cm
Radius of Gold circle=21/2=10.5 cm
Area of Gold region is given by
= πr^{2}= (22/7) (10.5)^{2}= 346.5 cm ^{2}
Now since each band is 10.5 cm wide
Radius of red ring= 10.5+ 10.5=21 cm
Now Radius of Red ring is given as
= π(21)^{2} - π(10.5)^{2} = 1386-346.5=1039.5 cm^{2}
Radius of Blue ring =21 +10.5=31.5 cm
Now Radius of Blue ring is given as
= π(31.5)^{2} - π(21)^{2} = 3118.5-1386=1732.5 cm^{2}
Radius of Black ring =31.5 +10.5=42 cm
Now Radius of Black ering is given as
= π(42)^{2} - π(31.5)^{2} = 5544-3118.5=2425.5 cm^{2}
Radius of White ring =42 +10.5=52.5 cm
Now Radius of Black ering is given as
= π(52.5)^{2} - π(42)^{2} = 8662.5-5544=3118.5 cm^{2} Question 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?

Solution:
Diameter of wheel is given as =80 cm
So radius of the wheel=40 cm
So circumference of wheel =2πr= 2(22/7)(40)= (1760/7)cm
So in 1 revolution, Car travels the distance (1760/7)cm
Now Speed of the Car= 66Km/h
=(66X1000)/60 meter/minute
=1100 meter/minute
=110000 cm/minute
This mean in simple term
Distance travelled in 1 min = 110000 cm
Distance travelled in 10 min=1100000 cm
So Total number of revolutions =( 1100000)/(1760/7)
=4375 Question 5. Tick the correct answer in the following and justify your choice : If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
(A) 2 units
(B) π units
(C) 4 units
(D) 7 units Solution:
Area of Circle = πr^{2}
Circumference of Circle =2πr
According to the question
πr^{2} = 2πr
r=2 units Download this assignment as pdf Also Read