Final answer:
The radius of each circle is 6x, since both circles are identical and the diameter of Circle B is 12x. The area of the circles is therefore π(6x)², making the correct answer B) π(6x)².
Step-by-step explanation:
The question states that the radius of Circle A is x + 4 and the diameter of Circle B is 12x, with both circles being identical. To find the area of the circles, we first need to establish their radius. Since the diameter is twice the radius, the radius of Circle B is ½ of 12x, which is 6x. With both circles being identical, this means the radius of Circle A must also equal 6x, hence x + 4 must equal 6x. Solving for x, we find that x equals 4, making the radius of the circles 6 × 4, which is 24.
The formula for the area of a circle is A = πr². Substituting the value of the radius into this formula, the area becomes A = π(24)² = π(576), so the area of the circles is π(576) which simplifies to π(6x)² when substituting back the value of x as 4. Therefore, the correct answer is B) π(6x)².