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Problems based on Perimeter and area of a circle
Areas Related To Circles
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 = ?
?
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
∵ 𝟗𝟎 𝐊𝐦= 90 x 1000 x 100 cm
= 9000000
25000
= 360 cm
2πr = 360 cm
2πr
Problems based on Perimeter and area of a circle
Hence, the radius of the wheel is 57.27cm
?
r = 57.27 cm
2 x 22 x r = 360cm
7
r = 360x7 cm 2x22
= 180 x 7
22
= 90 x 7
11
= 630
11
Q) The diameter of a cart wheel is 21 cm. How many revolutions will it make in moving 1.32 km?
Problems based on Perimeter and area of a circle
21 cm
Given: Diameter of the cart wheel = 21 cm
To Find: Number of revolutions = ? made in 1.32 Km
Solution: Let the radius of the cart wheel be ’r’.
Thus, r = Diameter = 21 cm
Problems based on Perimeter and area of a circle
21 cm
2 2
Circumference of the cart wheel = 2πr
= 2x22x21cm
7 2
= 462
7
= 66 cm
Converting 1.32 Km into cm, we get,
Problems based on Perimeter and area of a circle
21 cm
1.32 Km = 1.32 x 1000 m [∵ 1 Km = 1000 m]
= 1.32 x 1000 x 100 cm [∵1m = 100 cm]
= 132000 cm
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)
Hence, the cart wheel will make 2000 revolutions in moving
1.32 km.
2000
= 132000 cm
66 cm
= 12000
6
21 cm
=
Q) A wheel of a bicycle makes 6 revolutions per second. If the diameter of the wheel is 80 cm, find its speed.
Problems based on Perimeter and area of a circle
Given: Number of revolutions per second = 6 Diameter = 80cm
To find:
Speed = ?
Formula:
Speed = Distance
Time
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
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
Problems based on Perimeter and area of a circle
= 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
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.
Q) Find the radius of the circle whose perimeter and area are numerically equal.
Problems based on Perimeter and area of a circle
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.
Thus, πr2 = 2πr πr2 - 2πr = 0
Problems based on Perimeter and area of a circle
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
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