Find the diameter (in cm) of a circle whose circumference is equal to the sum of the circumferences of two circles of radii 12 cm and 16 cm.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 56.
We know that,
Circumference of the circle = 2πr
here, r = radius of the circle
Circumference of the first circle with radius 12 cm = 2π × 12 = 24π cm
Circumference of the second circle with radius 16 cm = 2π × 16 = 32π cm
Sum of the circumference of two circles = 24π + 32π = 56π
Now,
Let the radius of the required circle be x
Circumference = 2πx
⇒ 2πx = 56π
⇒ 2x = 56
⇒ x = 28 cm
So, The diameter of the circle = 2x = 2 × 28 = 56 cm