Math Problem Statement

Find the area A and circumference C of a circle of radius 44 meters. Question content area bottom Part 1 Aequals=enter your response here ▼ meters cubic meters square meters ​(Type an exact answer in terms of piπ​.) Part 2 Cequals=enter your response here ▼ cubic meters meters square meters ​(Type an exact answer in terms of piπ​.)

Solution

To find the area AA and the circumference CC of a circle with radius r=44r = 44 meters, we can use the following formulas:

  1. Area of a circle:
    A=πr2A = \pi r^2

  2. Circumference of a circle:
    C=2πrC = 2 \pi r

Part 1: Area AA

A=π(44)2=π×1936=1936πsquare metersA = \pi (44)^2 = \pi \times 1936 = 1936\pi \, \text{square meters}

So, the area is: A=1936πsquare metersA = 1936\pi \, \text{square meters}

Part 2: Circumference CC

C=2π×44=88πmetersC = 2\pi \times 44 = 88\pi \, \text{meters}

So, the circumference is: C=88πmetersC = 88\pi \, \text{meters}

Would you like more details or further explanations on any part?

Here are 5 related questions for you to explore:

  1. How would the area change if the radius was doubled?
  2. What is the numerical approximation of the area and circumference if π\pi is approximated as 3.14?
  3. What is the diameter of the circle?
  4. How does the area relate to the circumference for this circle?
  5. What is the ratio of the circumference to the radius of any circle?

Tip: The circumference of a circle is always proportional to its radius, with the constant of proportionality being 2π2\pi.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circles
Area of Circle
Circumference of Circle

Formulas

Area of a circle: A = πr^2
Circumference of a circle: C = 2πr

Theorems

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Suitable Grade Level

Grades 6-8