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.

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Accepted Answer

Step 1: Calculate the circumference of the first circle with radius 12 cm.   
Circumference = 2 * π * r = 2 * π * 12 = 24π cm

Step 2: Calculate the circumference of the second circle with radius 16 cm.
Circumference = 2 * π * r = 2 * π * 16 = 32π cm

Step 3: Sum of the circumferences = 24π + 32π = 56π cm

Step 4: Let the radius of the new circle be R. Its circumference is equal to the sum above:
2 * π * R = 56π

Step 5: Divide both sides by 2π:
R = 56π / (2π) = 28 cm

Step 6: Diameter = 2 * R = 2 * 28 = 56 cm

Therefore, the diameter of the circle is 56 cm.

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