Math Problem Statement

The diameter of a circle is 169 in. Find the circumference to the nearest whole number.

Solution

To find the circumference of a circle, we use the formula:

C=π×dC = \pi \times d

where:

  • CC is the circumference,
  • dd is the diameter,
  • π\pi is approximately 3.14163.1416.

Given that the diameter d=169ind = 169 \, \text{in}, we substitute this into the formula:

C=π×1693.1416×169C = \pi \times 169 \approx 3.1416 \times 169

C531.47inC \approx 531.47 \, \text{in}

Rounded to the nearest whole number:

C531inC \approx 531 \, \text{in}

So, the circumference of the circle is approximately 531 inches.


Would you like any further details or explanations on this?

Here are a few related questions:

  1. How would the circumference change if the diameter were doubled?
  2. What is the area of a circle if the diameter is 169 inches?
  3. How do you derive the formula for the circumference of a circle?
  4. What is the relationship between the radius and diameter of a circle?
  5. How can the circumference be calculated using the radius instead of the diameter?

Tip: If you ever need to estimate π\pi for rough calculations, using 3.143.14 as an approximation is often good enough!

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Math Problem Analysis

Mathematical Concepts

Geometry
Circles
Circumference

Formulas

C = π × d

Theorems

Circumference of a circle formula

Suitable Grade Level

Grades 6-8