Using the formula [tex]$C=2 \pi r$[/tex], find the circumference of a circle with diameter of 28 inches. Round your answer to the nearest inch.
A) 44 in .
B) 56 in .
C) 88 in .
D) 28 in .
Answer (1)
Calculate the radius of the circle by dividing the diameter by 2: r = 2 28 = 14 inches.
Substitute the radius into the circumference formula: C = 2 π r = 2 π ( 14 ) = 28 π inches.
Approximate the value of 28 π to get C ≈ 87.96 inches.
Round the circumference to the nearest inch: 88 inches .
Explanation
Calculate the circumference The formula for the circumference of a circle is given by C = 2 π r , where C is the circumference and r is the radius of the circle. We are given that the diameter of the circle is 28 inches. The radius is half of the diameter, so we can calculate the radius as follows: r = 2 d = 2 28 = 14 inches Now we can substitute the value of the radius into the circumference formula: C = 2 π r = 2 π ( 14 ) = 28 π inches To find the numerical value, we can use the approximation π ≈ 3.14159 . Therefore, C = 28 π ≈ 28 × 3.14159 ≈ 87.96452 inches Finally, we round the circumference to the nearest inch: C \approx 88 \text{ inches}$
State the final answer The circumference of the circle with a diameter of 28 inches, rounded to the nearest inch, is 88 inches.
Examples
Understanding the circumference of a circle is useful in many real-world situations. For example, if you're building a circular fence around a garden, knowing the circumference helps you determine how much fencing material you need. If the diameter of your garden is 28 feet, then the amount of fencing you need is approximately 88 feet. This ensures you purchase the correct amount of materials, saving time and money.
