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In Mathematics / College | 2025-07-04

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) 28 in .
B) 88 in .
C) 56 in .
D) 44 in .

Asked by dorthiepatton983

Answer (1)

Calculate the radius 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 π and calculate the circumference: C ≈ 28 × 3.14159 ≈ 87.96452 inches.
Round the circumference to the nearest inch: C ≈ 88 ​ inches.

Explanation

Problem Analysis We are given a circle with a diameter of 28 inches, and we need to find its circumference using the formula C = 2 π r , where C is the circumference and r is the radius.

Calculate the Radius First, we need to find the radius of the circle. The radius is half of the diameter. So, we calculate the radius as follows: r = 2 d ​ = 2 28 ​ = 14 The radius of the circle is 14 inches.

Apply the Circumference Formula Now, we substitute the value of the radius into the circumference formula: C = 2 π r = 2 π ( 14 ) = 28 π So, the circumference is 28 π inches.

Calculate the Circumference We can approximate the value of π as 3.14159. Therefore, the circumference is approximately: C = 28 × 3.14159 ≈ 87.96452

Round to the Nearest Inch Finally, we round the circumference to the nearest inch: C ≈ 88 Therefore, the circumference of the circle is approximately 88 inches.

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 scenarios. For example, if you're building a circular fence around a garden, knowing the circumference helps you determine how much fencing material you need. Similarly, if you're designing a circular race track, the circumference tells you the total distance a runner covers in one lap. These calculations ensure efficient planning and resource allocation in various projects.

Answered by GinnyAnswer | 2025-07-05

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