Find the exact circumference (in inches) and area (in square inches) of a circle whose diameter has length 18 in. circumference 56.52 X area 254.34 in2 X Need Help? Read It
The Correct Answer and Explanation is:
To find the circumference and area of a circle, we use two key formulas:
- Circumference formula: C=π×dC = \pi \times dC=π×d where CCC is the circumference and ddd is the diameter.
- Area formula: A=π×r2A = \pi \times r^2A=π×r2 where AAA is the area and rrr is the radius.
Step 1: Given Data
- Diameter of the circle, d=18d = 18d=18 inches.
From the diameter, we can calculate the radius rrr, since the radius is half the diameter: r=d2=182=9 inchesr = \frac{d}{2} = \frac{18}{2} = 9 \text{ inches}r=2d=218=9 inches
Step 2: Calculate the Circumference
Now, we can use the circumference formula: C=π×d=π×18C = \pi \times d = \pi \times 18C=π×d=π×18
Using the approximation π≈3.1416\pi \approx 3.1416π≈3.1416: C≈3.1416×18≈56.5488 inchesC \approx 3.1416 \times 18 \approx 56.5488 \text{ inches}C≈3.1416×18≈56.5488 inches
So, the circumference is approximately 56.55 inches.
Step 3: Calculate the Area
Next, we use the area formula: A=π×r2=π×(9)2A = \pi \times r^2 = \pi \times (9)^2A=π×r2=π×(9)2 A=π×81≈3.1416×81≈254.4696 square inchesA = \pi \times 81 \approx 3.1416 \times 81 \approx 254.4696 \text{ square inches}A=π×81≈3.1416×81≈254.4696 square inches
So, the area is approximately 254.47 square inches.
Final Answer
- The circumference of the circle is approximately 56.55 inches.
- The area of the circle is approximately 254.47 square inches.
Both results are rounded to two decimal places. These values are based on using π≈3.1416\pi \approx 3.1416π≈3.1416.
To find the circumference and area of a circle, we use two key formulas:
- Circumference formula: C=π×dC = \pi \times dC=π×d where CCC is the circumference and ddd is the diameter.
- Area formula: A=π×r2A = \pi \times r^2A=π×r2 where AAA is the area and rrr is the radius.
Step 1: Given Data
- Diameter of the circle, d=18d = 18d=18 inches.
From the diameter, we can calculate the radius rrr, since the radius is half the diameter: r=d2=182=9 inchesr = \frac{d}{2} = \frac{18}{2} = 9 \text{ inches}r=2d=218=9 inches
Step 2: Calculate the Circumference
Now, we can use the circumference formula: C=π×d=π×18C = \pi \times d = \pi \times 18C=π×d=π×18
Using the approximation π≈3.1416\pi \approx 3.1416π≈3.1416: C≈3.1416×18≈56.5488 inchesC \approx 3.1416 \times 18 \approx 56.5488 \text{ inches}C≈3.1416×18≈56.5488 inches
So, the circumference is approximately 56.55 inches.
Step 3: Calculate the Area
Next, we use the area formula: A=π×r2=π×(9)2A = \pi \times r^2 = \pi \times (9)^2A=π×r2=π×(9)2 A=π×81≈3.1416×81≈254.4696 square inchesA = \pi \times 81 \approx 3.1416 \times 81 \approx 254.4696 \text{ square inches}A=π×81≈3.1416×81≈254.4696 square inches
So, the area is approximately 254.47 square inches.
Final Answer
- The circumference of the circle is approximately 56.55 inches.
- The area of the circle is approximately 254.47 square inches.
Both results are rounded to two decimal places. These values are based on using π≈3.1416\pi \approx 3.1416π≈3.1416.
