Find the area of a quadrant of a circle whose circumference is 2
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    Areas Related to Circles

    Multiple Choice QuestionsShort Answer Type

    1. The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumference of two circles.
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    2. The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having its area equal to the sum of the areas of the two circles. 
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    Multiple Choice QuestionsLong Answer Type

    3. Fig. 12.3, depicts an archery target marked with its five scoring areas from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.


    Fig. 12.3
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    Multiple Choice QuestionsShort Answer Type

    4. The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?
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    5.

    Tick the correct answer in the following: If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
    (A) 2 units    (D) π units
    (C) 4 units    (D) 7 units.

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    6. Find the area of a sector of a circle with radius 6 cm and of angle 60°.
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    7. Find the area of a quadrant of a circle whose circumference is 22 cm.

    Here, we have

    Circumference = 22 cm

    rightwards double arrow space space space space space space space 2 πr space equals space 22 space cm

    rightwards double arrow space space straight r space space space equals space fraction numerator 22 over denominator 2 straight pi end fraction rightwards double arrow space space straight r space space space equals space fraction numerator 22 cross times 7 over denominator 2 cross times 22 end fraction rightwards double arrow space space straight r space space space equals space 3.5 space cm space space

    Now, Area of quadrant

    equals space 1 fourth πr squared equals space open parentheses 1 fourth cross times 22 over 7 cross times 3.5 cross times 3.5 close parentheses space space cm squared equals space space open parentheses fraction numerator 269.5 over denominator 28 end fraction close parentheses space cm squared space equals space 9.625 space space cm squared
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    8. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
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    9.

    A chord of circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding :

    (i) Minor segment
    (ii) Major sector.

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    10.

    In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find :

    (i)    the length of the arc
    (ii)    area of the sector formed by the arc
    (iii)    area of the segment formed by the corresponding chord.

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