Math Problem Statement

The radius of the circle is 11 cm, and point C is the center. Find the length of the diameter and the approximate circumference of the circle. 11 cm C Radius (cm) Diameter (cm) Circumference (cm) 11

Solution

To calculate the diameter and the approximate circumference of a circle given the radius:

  1. Diameter: The diameter is twice the radius.
    Diameter=2×Radius\text{Diameter} = 2 \times \text{Radius} Substituting the radius: Diameter=2×11=22cm\text{Diameter} = 2 \times 11 = 22 \, \text{cm}

  2. Circumference: The formula for the circumference is: Circumference=2π×Radius\text{Circumference} = 2 \pi \times \text{Radius} Using π3.14\pi \approx 3.14: Circumference=2×3.14×11=69.08cm\text{Circumference} = 2 \times 3.14 \times 11 = 69.08 \, \text{cm}

Final Values:

Radius (cm)Diameter (cm)Circumference (cm)
112269.08

Would you like a detailed explanation of these calculations or further assistance? 😊


Follow-Up Questions:

  1. How is the relationship between radius, diameter, and circumference derived?
  2. What is the exact circumference using π=3.14159\pi = 3.14159?
  3. Can you calculate the area of this circle?
  4. What would the circumference be if the radius were doubled?
  5. How can you use the circumference to approximate the area of a circle?

Tip: Always remember that π\pi is an irrational number, so calculations involving it are approximations unless left in terms of π\pi.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circle properties

Formulas

Diameter = 2 × Radius
Circumference = 2π × Radius

Theorems

Basic geometric properties of circles

Suitable Grade Level

Grades 5-7