Math Problem Statement

Find the radius given that the circumference of a circle is 15.7 km and pi is 3.14.

Solution

The problem provides the circumference of a circle C=15.7kmC = 15.7 \, \text{km} and asks to find the radius rr, using π=3.14\pi = 3.14.

The formula for the circumference of a circle is:

C=2πrC = 2\pi r

We can solve for rr by rearranging the formula:

r=C2πr = \frac{C}{2\pi}

Substitute C=15.7kmC = 15.7 \, \text{km} and π=3.14\pi = 3.14:

r=15.72×3.14=15.76.28r = \frac{15.7}{2 \times 3.14} = \frac{15.7}{6.28}

Now, let's calculate the value of rr.The radius rr of the circle is 2.5km2.5 \, \text{km}.

Would you like more details or have any questions?

Here are five related questions to deepen your understanding:

  1. How would the formula for the radius change if you had the diameter instead of the circumference?
  2. What would the radius be if the circumference was doubled?
  3. How can you calculate the area of the circle using the radius you just found?
  4. What is the relationship between the radius and the diameter of a circle?
  5. How does using a more precise value for π\pi affect the accuracy of the radius calculation?

Tip: The radius is always half the diameter, so knowing one helps you find the other easily.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circles
Radius
Circumference

Formulas

C = 2πr
r = C / 2π

Theorems

Circumference Theorem

Suitable Grade Level

Grades 6-8