The radii of two circles are 19 cm and 9 cm respectively. Find t
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    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.

    Let the radius of the bigger circle be R cm. and radii of two smaller circles are r1and r2, then according to question.

    2πR = 2πr1 + 2πr2
    ⇒    2πR = 2π (19) + 2π (9)
    ⇒    2πR = 2π (19 + 9)
    ⇒    R = 28
    Hence, radius of the circle be 28 cm.

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    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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    Answer
    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

    We have,
    r = Radius of the region representing Gold score = 10.5 cm
    ∴ r1 = Radius of the region representing Gold and Red scoring areas = (10.5 + 10.5) cm = 21 cm = 2r cm
    r2 = Radius of the region representing Gold, Red and Blue scoring areas = (21 + 10.5) cm = 31.5 cm = 3r cm
    r3 = Radius of the region representing Gold, Red, Blue and Black scoring areas = (31.5 + 10.5) cm = 42 cm = 4r cm
    r4 = Radius of the region representing Gold, Red, Blue, Black and white scoring areas = (42 + 10.5) cm = 52.5 cm = 5r cm
    Now, A, = Area of the region representing Gold scoring area

    equals space πr space equals space 22 over 7 straight x left parenthesis 10.5 right parenthesis squared equals 22 over 7 straight x 10.5 space cross times space 10.5
    = 22 × 1.5 × 10.5 = 346.5 cm2
    A2 = Area of the region representing Red scorring area
    = π (2r)2 - πr2 = 3πr2 = 3A1
    = 3 × 346.5 cm2 = 1039.5 cm2
    A3 = Area of the region representing Blue scoring area
    = π(3r)2 - π(2r)2 = 9πr2 - 4πr2
    = 5πr2 = 5A1 = 5 × 346.5 cm2
    = 1732.5 cm2
    A4 = Area of the region representing black scoring area
    = π(4πr)2 - π(3r)2 = 7πr2 = 7A1
    =7 × 346.5 cm2 = 2425.5 cm2
    A1 = Area of the region representing white scoring area
    = π(5r)2 - π(4r)2 - 9πr2 = 9 A1
    = 9 × 346.5 cm2 = 3118.5 cm2
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    Answer

    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.

    Let r be the radius of the circle then,
    Perimeter = 2 πr
    and Area = πr2
    It is given that
    Perimeter of circle = Area of circle
    ⇒ 2πr = πr2
    ⇒    r = 2 units
    Hence, right option be (A): 2 units.

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    Answer
    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. 

    Let the radius of the required circle be R and radii of two given circles be r1 and r2, then according to question.
    πR2 = πr12 + πr22
    ⇒    πR2 = (r12 + r22)
    ⇒    R2 = 64 + 36
    ⇒    R2 = 100
    ⇒    R = 10 cm.

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    Answer
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