Circumference and Area of Circle

A circle is a plane geometrical figure, every point of which is at a constant distance from a fixed point in the same plane. A line segment with its end-points lying on a circle is called chord of the circle. Diameter is the longest chord in a circle. A line passing through a circle and intersecting the circle at two different points is known as a secant of the circle.

The distance covered by moving once around a circle is called its perimeter or circumference. The circumference of a circle is equal to two times the product of pi and its radius. The measure of a surface, enclosed by the circumference of the circle, is called its area. Area of a circle is equal to the product of pi and square of its radius.

The portion (or part) of a circular region enclosed by two radii and the corresponding arc is called a sector of the circle. The portion (or part) of a circular region enclosed between a chord and the corresponding arc is called a segment of the circle. Area of major sector is the difference of area of circle and area of minor sector. Area of minor sector is the difference of area of circle and area of major sector.

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  • Q1

    Which of the following figures shows a chord?

    Marks:1
    Answer:

    Explanation:

    A chord connects two points on the circle. So the correct figure is:

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  • Q2

    The ratio of the circumference and the diameter of a circle is

    Marks:1
    Answer:

    π

    Explanation:

    The ratio of the circumference and the diameter of a circle =  2πr/ 2r = π

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  • Q3

    If the angle of the sector is 30°, then what is the area of the sector of a circle of radius 7cm?

    Marks:1
    Answer:

    12.833 cm2

    Explanation:

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  • Q4

    Area of a sector of a circle of radius 4 cm is 4πcm2. What is the angle of the sector of the circle?

    Marks:1
    Answer:

    π/2

    Explanation:

    Area of the sector = 4πcm2

    Let θ be the angle of the sector.

    Area of the sector = (θ/2π)πr2

    (θ/2π)π(4)2 = 4π

    θ = π/2

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  • Q5

    A circular track is formed between two concentric circles of radii 7m and 14m. What is the area of the track?

    Marks:1
    Answer:

    147π m2

    Explanation:

    Area of the circle of radius 7m = π r2

    = π(7)2 m2

    =49π m2

    Area of the circle of radius 14m = π R2

    = π 142 m2

    =196π m2

    Area of the track = 196π m2 – 49π m2

    = 147π m2

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