1.
Areas Related To Circles
Problems based on
Perimeter and area of a circle
Chapter : Areas Related To Circles Website: www.letstute.com

2.
Problems based on
Perimeter and area of a circle
Q) A wheel rotates 25000 times to cover a distance of 90 km. Find its
radius.
Given: Rotation of the wheel = 25000 times
Distance covered = 90 km
by the wheel
To find: Radius of the wheel = ?
?
Chapter : Areas Related To Circles Website: www.letstute.com

3.
Problems based on
Perimeter and area of a circle
Solution:
Let ‘r’ be the radius of the wheel.
?
Circumference
of the wheel
= Distance covered in
one rotation.
= 90 Km
2πr
∵ ퟗퟎ 퐊퐦= 90 x 1000 x 100 cm
= 9000000
25000
= 360 cm
2πr = 360 cm
Chapter : Areas Related To Circles Website: www.letstute.com

4.
Problems based on
Perimeter and area of a circle
2 x 22 x r
= 360cm
r = 360x7 cm
2x22
= 180 x 7
22
= 90 x 7
11
= 630
11
r = 57.27 cm
7
Hence, the radius of the wheel is 57.27cm
?
Chapter : Areas Related To Circles Website: www.letstute.com

5.
Problems based on
Perimeter and area of a circle
Q) The diameter of a cart wheel is 21 cm. How many revolutions
will it make in moving 1.32 km?
21 cm
Given: Diameter of the cart wheel = 21 cm
To Find: Number of revolutions = ?
made in 1.32 Km
Chapter : Areas Related To Circles Website: www.letstute.com

6.
Problems based on
Perimeter and area of a circle
Solution: Let the radius of the cart wheel be ’r’.
Thus, r = Diameter = 21 cm
2 2
Circumference of the cart wheel = 2πr
= 2x22x21cm
7 2
= 462
7
= 66 cm
21 cm
Chapter : Areas Related To Circles Website: www.letstute.com

7.
Problems based on
Perimeter and area of a circle
21 cm
Converting 1.32 Km into cm, we get,
1.32 Km = 1.32 x 1000 m [∵ 1 Km = 1000 m]
= 1.32 x 1000 x 100 cm [∵1m = 100 cm]
= 132000 cm
Chapter : Areas Related To Circles Website: www.letstute.com

8.
Problems based on
Perimeter and area of a circle
Number of revolutions = Total distance covered
Circumference (Distance covered by
1 round of the cart wheel)
= 132000 cm
66 cm
= 12000
6
2000
21 cm
=
Hence, the cart wheel will make 2000 revolutions in moving
1.32 km.
Chapter : Areas Related To Circles Website: www.letstute.com

9.
Problems based on
Perimeter and area of a circle
Q) A wheel of a bicycle makes 6 revolutions per second. If the
diameter of the wheel is 80 cm, find its speed.
Given: Number of revolutions per second = 6
Diameter = 80cm
To find: Speed = ?
Formula: Speed = Distance
Time
Chapter : Areas Related To Circles Website: www.letstute.com

10.
Problems based on
Perimeter and area of a circle
Solution: Let the radius of the wheel be denoted as ‘r’.
Thus, r = Diameter = 80 = 40 cm
2 2
Circumference of the wheel = 2 πr
= 2x22x 40 cm
7
= 1760
7
= 251.42cm
Chapter : Areas Related To Circles Website: www.letstute.com

11.
Problems based on
Perimeter and area of a circle
Distance covered in 1 revolution = circumference = 251.42cm
Distance covered in 6 revolutions
= 6 x Distance covered in 1 revolution
= 6 x 251.42 cm
= 1508.52 cm
Since, 1 m = 100 cm
?m = 1508.52 cm
= 1508.52 cm
100
= 15.08 m
∵ 15.08 m = 1508.52 cm
Chapter : Areas Related To Circles Website: www.letstute.com

12.
Problems based on
Perimeter and area of a circle
Speed = Distance
Time
= 15.08 m
1 second
Result: Speed = 15.08 m/second
Hence, the speed of the wheel is 15.08m/second.
Chapter : Areas Related To Circles Website: www.letstute.com

13.
Problems based on
Perimeter and area of a circle
Q) Find the radius of the circle whose perimeter and area are
numerically equal.
Given: Perimeter and the area of the circle are equal
To Find: Radius of the circle = ?
Solution: Let ‘r’ be the radius of the circle.
Then, its area = πr2 and
its perimeter = 2πr
It is given that the area of the circle is numerically equal to its
perimeter.
Chapter : Areas Related To Circles Website: www.letstute.com

14.
Problems based on
Perimeter and area of a circle
Thus, πr2 = 2πr
πr2 - 2πr = 0
πr(r-2) = 0
Either πr = 0 or
r-2 = 0
r = 0 (rejected) or
r = 2
Hence, the radius of the circle is 2 units
Chapter : Areas Related To Circles Website: www.letstute.com

15.
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