Find the diameter of a circle whose area is equal to the sum of the areas of circles with radius 3 and 4.
| July 22, 2021 | education
The area of a circle is determined by the formula: S = πR ^ 2, where R is the radius of this circle.
The area of a circle with a radius of 3 is: S1 = π * 3 ^ 2 = 9π.
The area of a circle with a radius of 4 is: S2 = π * 4 ^ 2 = 16π.
The sum of the areas of these circles: S3 = S1 + S2 = 9π + 16π = 25π.
The radius of a circle with an area of 25π:
R ^ 2 = S3 / π = 25π / π = = 25;
R = √25 = 5.
Accordingly, the diameter of this circle is D = 2R = 2 * 5 = 10.
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