iCoachMath.com: Examples on Circumference and Arc Length - Polygons and Circles

Curriculum: Idaho Content Standards Click to change Curriculum

Topic: Polygons and Circles Click to change Topic

Lesson: 9.M.2.1.1-2, 10.M.2.1.1-2: Circumference and Arc Length Click to change Lesson

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e Find the circumference of the circle whose radius is 5.2 cm. e

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e The circumference of a circle is 20π cm. Find its radius. e

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e The diameter of a cart wheel is 2.3 m. How much distance will it cover if it makes 20 revolutions?
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e The radius of a bicycle wheel is 60 cm. How many revolutions does the wheel make when the bicycle travels 360 m? [Take π = 3.] e

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e Circumference of a circle is given as 42π m. Find the radius of the circle. e

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e Find the length of the arc of a semicircle whose radius is 5 in..
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e If the diameter of the circle shown is 20 in., then find the length of arc MN. e

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e Find the length of arc RP from figure. [Given: (x₁, y₁) = (-3, 1) and (x₂, y₂) = (0, 5).] e

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e If m∠θ = 10 and AB = 3 units, then find the length of arc BX.
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e The length of an arc is 2π cm and its measure is 120^o. Find the radius of the circle. e

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e Find the perimeter of the shaded portion in the figure, given OA(r) = 8. [Take π = 3.] e

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e Find the length of the arc l from the figure. [Given r₁ = 5, r₂ = 9, s₁ = 6.]
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e The circumference of a circle is 35 ft. what is the radius of the circle?
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e In the diagram the ratio of the length of Arc AB to length of Arc CD is 4 : 3. What is the ratio of m to n? e

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e Find the circumference of the circle. [Given x = 45, r = 30.] e

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e Length of the arc AB is given as 6π cm and the measure of arc AB is 15. Find the circumference of the circle.
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e Find the value of x from the figure. [Given a = 4, b = 3 and m = 45.] e

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e If r = 2 in., find the length of arc AB. e

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e An athlete was running on a circular track of diameter 80 m. He first started at a point and ran 23 distance of the track length, in clockwise direction and ran 13 distance of the track length, in anti clockwise direction. Find the total distance he ran. [Approximate the distance to the nearest integer.] [Take π = 3.] e

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e The circumference of a circle is 100π cm. Find the length of an arc whose measure is 72^o. e

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e Find the circumference of a circle in which a right triangle of base (b) 16.5 cm and height (h) 22 cm is inscribed. [Take π = 3.] e

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e Find the perimeter of the figure if a = 2.50 cm, b = 10 cm, c = 9 cm. e

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e Semi circles are drawn on a line of length 2 m as shown. The first semicircle has a radius of 12 cm. Radius of each consecutive semicircle is half the radius of the preceding semi circle. What is the sum of the arc lengths of all the semicircular portions?
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e Find the perimeter of the figure.
[Take α = 77^o, β = 159^o, a = 6 cm, b = 5 cm.] e

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e Find the circumference of the circle. [Given x = 36, r = 36.] e

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e A boy is playing with a ring of diameter 100 cm. It rolled down from his hands and made 18 revolutions while moving in a straight line and then came to stop. The boy normally covers a distance of 0.4 m in one step. How many steps he has to move to collect the ring? [Take π = 3.] e

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e The numerical value of the circumference of a circle is more than the numerical value of its area. What can be the best description of the radius of the circle? e

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e Length of the arc AB is given as 9π cm and the measure of arc AB is 60. Find the circumference of the circle.
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e The circumference of a circle is 20 ft. what is the radius of the circle?
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e The circumference of a circle is equal to its area in numerical value. Find the circumference of the circle. e

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e In the diagram the ratio of the length of Arc AB to length of Arc CD is 5 : 4. What is the ratio of m to n? e

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e Find the circumference of the circle. [Given x = 30, r = 60.] e

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e In fig the three circles are of same radius. Find the area of the shaded region. [Given r = 7 in..] e

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e The circumference of a circle is _______ times the diameter. e

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e Find the circumference of the circle whose radius is 4.9 cm. e

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e The circumference of a circle is 18π cm. Find its radius. e

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e A motor cycle wheel is designed with the rim diameter of 16 inches and tyre radius of 8.3 inches. Find the allowance for the air gap between the rim and the tyre. e

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e The circumference of a circle is 80π cm. Find the length of an arc whose measure is 36^o. e

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e In fig the three circles are of same radius. Find the area of the shaded region. [Given r = 5 in..] e

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e Two skaters are ready to skate on a cicular skating platform. Skater A is at a distance of 3 m from the center and skater B is at a distance of 6 m from the center. After 10 revolutions of their skating, how much distance would have B traveled more than A? Give answer in terms of π.
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e The diameter of a cart wheel is 5.3 m. How much distance will it cover if it makes 30 revolutions?
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e The radius of a bicycle wheel is 50 cm. How many revolutions does the wheel make when the bicycle travels 270 m? [Take π = 3.] e

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e Circumference of a circle is given as 38π m. Find the radius of the circle. e

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e Find the length of the arc of a semicircle whose radius is 4 cm.
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e If the diameter of the circle shown is 12 in., then find the length of arc MN. e

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e The length of an arc is 2π cm and its measure is 90^o. Find the radius of the circle. e

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e Arrange the arcs in the figure in the ascending order of its lengths. e

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e Find the perimeter of the shaded portion in the figure, given OA(r) = 12. [Take π = 3.] B

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B Find the circumference of a circle in which a right triangle of base (b) 13.5 cm and height (h) 18 cm is inscribed. [Take π = 3.] B

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B Three cyclists P, Q and R with the same speed starts from A to reach E as shown in the figure. P will follow the circular route AB-BC-CD-DE; Q will follow the route AC-CE and R will follow the route AE. Who will reach point E first? [Take a = 6.]
B

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B Find the length of arc RP from figure. [Given: (x₁, y₁) = (1, 5) and (x₂, y₂) = (1, 9).] B

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B If m∠θ = 10 and AB = 2 units, then find the length of arc BX.
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B Find the length of the arc l from the figure. [Given r₁ = 6, r₂ = 9, s₁ = 6.]
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B Find the perimeter of the figure if a = 2.50 cm, b = 8 cm, c = 7 cm. B

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B Select the correct statement / statements.
I. When a square is inscribed in a circle, the perimeter of the square is always less than the perimeter of the circle.
II. When a circle is inscribed in a square, the perimeter of the circle will be less than the perimeter of the square if the radius of the circle is greater than 2.
III. When a circle is inscribed in a square, the perimeter of the circle will be always less than the perimeter of the square. B

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B Semi circles are drawn on a line of length 8 m as shown. The first semicircle has a radius of 18 cm. Radius of each consecutive semicircle is half the radius of the preceding semi circle. What is the sum of the arc lengths of all the semicircular portions?
B

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B Find the value of x from the figure. [Given a = 6, b = 5 and m = 30.] B

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B Two skaters are ready to skate on a cicular skating platform. Skater A is at a distance of 2 m from the center and skater B is at a distance of 4 m from the center. After 6 revolutions of their skating, how much distance would have B traveled more than A? Give answer in terms of π.
B

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B Find the perimeter of the figure. [Take a = 4 cm, b = 6 cm, π = 3.] B

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B Ebin bakes a christmas cake in a 30 cm diameter tin. He has a 100 cm length of decorative band to go around the outer line of the cake. Is this band long enough? [Take π = 3.]
B

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B Find the perimeter of the figure.
[Take α = 84^o, β = 159^o, a = 6 cm, b = 5 cm.] B

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B Length of the arc AB is given as 9π cm and the measure of arc AB is 45. Find the circumference of the circle.
B

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