The radii of two circles are 8 cm and 15 cm.The perimeter of the circle having area equal to the sum of the areas of the two circles (in cm) is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 34π.
The radius of the first circle (r) = 8 cm
Area of the first circle = π(r)2 = π(8)2 = 64π cm2
The radius of the second circle (r1) = 15 cm
Area of the second circle = π(r1)2 = π(15)2 = 225π cm2
Total area of two circles = 64π + 225π = 289π cm2
Let the radius of the new circle be R cm.
So, πR2 = 289π
⇒ R2 = 289
⇒ R = √289 = 17 cm
Perimeter of the new circle = 2πR = 2 × π × 17 = 34π cm
Therefore, the perimeter of the circle with the combined area (in cm) is 34π.