2. The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the area

Question

2. The radii of two circles are 8 cm and 6 cm respectively. Find
the radius of the circle having area equal to the sum of the
areas of the two circles.

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Kylie 3 weeks 2021-10-01T14:05:16+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-01T14:06:25+00:00

    Answer:

    10

    Step-by-step explanation:

    area of first circle + area of second circle = final area of circle

    8^2 + 6^ 2 = R^ 2

    R = 10cm

    0
    2021-10-01T14:07:11+00:00

    Given:

    The radii of two circles are 8 cm and 6 cm.

    To be found:

    The radius of the circle having an area equal to the sum of the  areas of the two circles.

    Here are steps-

    • First, we will find the area of the two circles whose radii are given.
    • Adding the areas of two circles
    • We will get the area of the big circle.
    • And with the help of the area formula of the circle.

    So,

    Area of circle whose radius = 8cm

    Area = πr² unit sq. [∵ In which ‘r’ is the ‘radius’ of the circle]

    \boxed{= \pi \times (8)^{2} = \bf 64 \pi\ unit\ sq.}

    Area of circle whose radius = 8cm

    \boxed{= \pi \times (6)^{2} = \bf 36 \pi\ unit\ sq.}

    Now, the sum of the areas of circles will be

    = 64π + 36π = 100π units sq.

    Therefore,

    The area of the big circle = 100π unit sq.

    So,

    Area of the big circle = 100π unit sq.

    \pi r^{2} = 100 \pi

    \not{\pi} r^{2}= 100 \not{\pi}

    r= \sqrt{100}

    ⇒ r = 10 cm

    Hence,

    The radius of the big circle whose area equal to the sum of the  areas of the two circles = 10 cm.

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