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



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 = ?

?



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



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



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



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



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



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

=



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



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



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



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



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 = ?



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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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.