How to Find the Area of a Circle from the Diameter

Step-by-step solution

1. Halve the diameter to get the radius.

   $$r = \frac{12}{2} = 6$$

   Why: The area formula needs the radius, and the radius is half the diameter.

2. Write the area formula.

   $$A = \pi r^2$$

   Why: The area depends on the radius squared.

3. Substitute the radius and simplify.

   $$A = \pi(6)^2 = 36\pi$$

   Why: Six squared is 36. Keep pi for the exact answer.

4. Estimate with pi about 3.14.

   $$36 \times 3.14 \approx 113.1$$

   Why: The estimate confirms the order of magnitude.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

1. 1

   $d = 10$

   Show answer

   $A = 25\pi$

2. 2

   $d = 4$

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   $A = 4\pi$

3. 3

   $d = 8$

   Show answer

   $A = 16\pi$

4. 4

   $d = 20$

   Show answer

   $A = 100\pi$

5. 5

   $d = 14$

   Show answer

   $A = 49\pi$