Question

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 two circles.

Answer 1

Given,

Radii of the two circles are 6 cm and 8 cm

Area of circle with radius 8 cm = π (8)² = 64π cm²

Area of circle with radius 6cm = π (6)² = 36π cm²

Sum of areas = 64π + 36π = 100π cm²

Let the radius of the circle be x cm

Area of the circle = 100π cm² (from above)

πx² = 100π

x = √100 = 10 cm

Therefore, the radius of the circle is 10 cm.