Final answer:
Using the formula for the area of a circle, we first find the radius, which is 6 units. Since the diameter of a circle is twice its radius, the diameter of this particular circle is 12 units.
Step-by-step explanation:
The student wants to find the diameter of a circle whose area is 36π. This falls under the sphere of Mathematics, specifically geometry. We can use the formula for the area of a circle, which is A = πr² to solve this problem. Here A represents the area, π is a constant (approximately 3.14159), and r represents the radius of the circle.
Since the area of the circle in the question is given as 36π, we can form the equation: 36π = πr². Cancelling out π from both sides, we're left with 36 = r². Now, taking the square root of both sides yields r = √36, which simplifies to r = 6. The radius of the circle is thus 6 units.
However, we're tasked with finding the diameter of the circle. The diameter is simply twice the radius, so in this case, d = 2r = 2*6, which equals 12. Therefore, the correct answer is b) 12.
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