The area of circle A is equal to the sum of the area of two small circles with diameters of 6cm and 8cm. Then the diameter of circle A will be? 5 10 15 20

To solve this problem, we first need to understand the formula for the area of a circle, which is πr², where r is the radius of the circle.

Step 1: Calculate the radius of the two smaller circles. The radius is half of the diameter, so the radii of the smaller circles are 3cm and 4cm.

Step 2: Calculate the area of the two smaller circles. Using the formula for the area of a circle:

Area of smaller circle 1 = π(3cm)² = 9π cm² Area of smaller circle 2 = π(4cm)² = 16π cm²

Step 3: Add the areas of the two smaller circles together. This will give us the area of the larger circle A.

Area of circle A = 9π cm² + 16π cm² = 25π cm²

Step 4: Now we need to find the radius of circle A. We know that the area of circle A is 25π cm², so we can set up the equation 25π = πr² and solve for r.

25 = r² r = 5cm

Step 5: The diameter of a circle is twice the radius, so the diameter of circle A is 2 * 5cm = 10cm.

So, the diameter of circle A is 10cm.