Math Problem Statement

Calculate the circumference of circles with given radii using specified values of π (π = 3.14 and π = 22/7).

Solution

Let's solve the problems given in the image:


Problem 2:

  • The radius of the circle is r=3cmr = 3 \, \text{cm}.
  • Use π3.14\pi \approx 3.14.
  • Circumference formula:
    Circumference=2πr\text{Circumference} = 2 \pi r
    Substituting the values:
    Circumference=2×3.14×3=18.84cm\text{Circumference} = 2 \times 3.14 \times 3 = 18.84 \, \text{cm}

Problem 4:

  • The radius of the circle is r=7cmr = 7 \, \text{cm}.
  • Use π227\pi \approx \frac{22}{7}.
  • Circumference formula:
    Circumference=2πr\text{Circumference} = 2 \pi r
    Substituting the values:
    Circumference=2×227×7\text{Circumference} = 2 \times \frac{22}{7} \times 7
    The 7 in the numerator and denominator cancel out:
    Circumference=2×22=44cm\text{Circumference} = 2 \times 22 = 44 \, \text{cm}

Summary of answers:

  1. For the first circle (radius = 3 cm), the circumference is 18.84 cm.
  2. For the second circle (radius = 7 cm), the circumference is 44 cm.

Do you want further explanation or details? Here are five related questions to deepen your understanding:

  1. What is the formula for calculating the area of a circle, and how would you use it for these examples?
  2. How does the choice of different approximations for π\pi affect the results?
  3. Can you derive the formula for circumference from the definition of π\pi?
  4. What would be the circumference of a circle with radius 5 cm using both 3.143.14 and 227\frac{22}{7} for π\pi?
  5. Why is π\pi often approximated as both 3.143.14 and 227\frac{22}{7}?

Tip: Always ensure to use the same value of π\pi throughout your calculations to avoid inconsistencies!

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Math Problem Analysis

Mathematical Concepts

Geometry
Circumference of Circles

Formulas

Circumference formula: C = 2πr

Theorems

Definition of π as the ratio of a circle's circumference to its diameter

Suitable Grade Level

Grades 5-7