Question

Q. 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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Answer 1

Step-by-step explanation:

consider two circles of radii R1 and R2 respectively {where R1=8cm and R2=6cm}

let R3 be the radius of third circle.

Area of first circle+Area of second circle=Area of third circle

=π×R1 square + π×R2 square=π×R3 square

=22/7×8 square+22/7×6 square=22/7 ×R3 square

=1408/7+792/7=22/7×R3 square

=201.14+113.14=22/7×R3 square

=314.2=3.142×R3 square

=R3 square×3.142=314.2

=R3 square=314.2/3.142

=R3 square=100CM

=R3=10cm

Hence, radius of third circle R3=10cm.