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 area of the two smaller circles.

The radius of the first small circle is 6cm/2 = 3cm. So, its area is π(3cm)² = 9π cm².

The radius of the second small circle is 8cm/2 = 4cm. So, its area is π(4cm)² = 16π cm².

Step 2: Add the areas of the two smaller circles together.

9π cm² + 16π cm² = 25π cm².

This is the area of circle A.

Step 3: Use the area of circle A to find its radius.

We know that the area of a circle is πr². So, we can set up the equation 25π cm² = πr² and solve for r.

Dividing both sides by π gives us r² = 25 cm², and taking the square root of both sides gives us r = 5 cm.

Step 4: Double the radius to find the diameter of circle A.

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

So, the diameter of circle A is 10 cm.