Question

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.

Answer 1

Answer :      Area of first circle = πr^2

= π82 = 64π sq cm

Area of second circle = π62 = 36π sq cm

As per question; area of the largest circle = 64π + 36π

= 100π sq cm

Or, πr2 = 100π

Or, r2 = 100

Or, r = 10 cm

Answer 2

Area of 1st circle = πr² = 64π cm²

Area of 2nd circle = πr² = 36π cm²

Area of the largest circle = 64π + 36π = 100π cm²

=> πr² = 100π (π got cancelled)

=> r² = 100

=> r = 10 cm