Areas related to circles - Perimeter and area of a circle for class 10 maths.
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Transcript of Areas related to circles - Perimeter and area of a circle for class 10 maths.
Areas Related To Circles
Problems based onPerimeter and area of a circle
Chapter : Areas Related To Circles Website: www.letstute.com
Problems based onPerimeter and area of a circle
Chapter : Areas Related To Circles Website: www.letstute.com
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 kmby the wheel
To find: Radius of the wheel = ?
?
Problems based onPerimeter and area of a circle
Chapter : Areas Related To Circles Website: www.letstute.com
Let ‘r’ be the radius of the wheel.Solution:
?Circumference of the wheel
= Distance covered in one rotation.= 90 Km
= 90 x 1000 x 100 cm = 9000000 25000 = 360 cm
2πr = 360 cm
2πr
Problems based onPerimeter and area of a circle
Chapter : Areas Related To Circles Website: www.letstute.com
r = 360x7 cm 2x22
Hence, the radius of the wheel is 57.27cm
?
r = 57.27 cm
2 x 22 x r 7
= 360cm
= 180 x 7 22= 90 x 7 11= 630 11
Problems based onPerimeter and area of a circle
Chapter : Areas Related To Circles Website: www.letstute.com
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
Problems based onPerimeter and area of a circle
Chapter : Areas Related To Circles Website: www.letstute.com
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
= 66 cm
21 cm
= 462 7
Problems based onPerimeter and area of a circle
Chapter : Areas Related To Circles Website: www.letstute.com
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
Problems based onPerimeter and area of a circle
Chapter : Areas Related To Circles Website: www.letstute.com
Number of revolutions = Total distance covered Circumference (Distance covered by 1 round of the cart wheel)
= 132000 cm 66 cm
Hence, the cart wheel will make 2000 revolutions in moving 1.32 km.
2000
= 12000 6
21 cm
=
Problems based onPerimeter and area of a circle
Chapter : Areas Related To Circles Website: www.letstute.com
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
80 cm
Problems based onPerimeter and area of a circle
Chapter : Areas Related To Circles Website: www.letstute.com
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
= 251.42cm
= 1760 7
80 cm
Problems based onPerimeter and area of a circle
Chapter : Areas Related To Circles Website: www.letstute.com
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
Distance covered in 1 revolution = circumference = 251.42cm
80 cm
Problems based onPerimeter and area of a circle
Chapter : Areas Related To Circles Website: www.letstute.com
Speed = Distance Time
= 15.08 m 1 second
Result: Speed = 15.08 m/second
Hence, the speed of the wheel is 15.08m/second.
80 cm
Problems based onPerimeter and area of a circle
Chapter : Areas Related To Circles Website: www.letstute.com
Q) Find the radius of the circle whose perimeter and area are numerically equal.
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.
Given: Perimeter and the area of the circle are equal
To Find: Radius of the circle = ?
Problems based onPerimeter and area of a circle
Chapter : Areas Related To Circles Website: www.letstute.com
Thus, πr2 = 2πr πr2 - 2πr = 0πr(r-2) = 0Either 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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