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) 56 in .
B) 88 in .
C) 44 in .
D) 28 in .
Answer (1)
Find the radius by dividing the diameter by 2: r = 2 28 = 14 inches.
Substitute the radius into the circumference formula: C = 2 π ( 14 ) = 28 π inches.
Calculate the circumference: C = 28 π ≈ 87.96 inches.
Round the circumference to the nearest inch: C ≈ 88 inches. The circumference of the circle is 88 inches.
Explanation
Problem Analysis We are given a circle with a diameter of 28 inches. We need to find the circumference using the formula C = 2 π r , where C is the circumference and r is the radius of the circle.
Calculate the Radius First, we need to find the radius of the circle. The radius is half of the diameter. So, we have: r = 2 d = 2 28 = 14 inches
Apply the Circumference Formula Now, we can substitute the value of the radius into the circumference formula: C = 2 π r = 2 π ( 14 ) = 28 π
Calculate the Circumference We can approximate π as 3.14159, but to get the most accurate rounded answer, we'll use the value of 28 π directly. The result of the operation is approximately 87.96459430051421. Rounding this to the nearest inch, we get 88 inches.
Final Answer Therefore, the circumference of the circle is approximately 88 inches.
Examples
Understanding circumference 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. Similarly, if you're designing a circular track, the circumference tells you the distance a runner covers in one lap. These calculations ensure you have the right amount of materials and accurate measurements for your projects.
