Math Problem Statement

The area of a circle can be found by evaluating the expression \pi r^{2} where r represents the radius of the circle.

Find the area of a circle with a radius of 7

Hint: Which should you do first? \pi\cdot ror r^{2}

Solution

To find the area of a circle using the formula:

A=πr2A = \pi r^2

where rr is the radius, follow these steps:

  1. First, square the radius rr. For a circle with radius r=7r = 7: r2=72=49r^2 = 7^2 = 49

  2. Then, multiply by π\pi: A=π×49A = \pi \times 49

So, the exact area is 49π49\pi.

To approximate the area using π3.1416\pi \approx 3.1416:

A49×3.1416=153.9384A \approx 49 \times 3.1416 = 153.9384

Thus, the approximate area of the circle is 153.94153.94 square units.

Would you like to go over any part in more detail?

Here are 5 related questions for further practice:

  1. What is the area of a circle with a radius of 10?
  2. How would the area change if the radius was doubled?
  3. What happens to the area if the radius is halved?
  4. If the area of a circle is 78.578.5, what is the radius?
  5. Can you find the circumference of a circle with a radius of 7?

Tip: Always remember to square the radius first before multiplying by π\pi when finding the area of a circle.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area of a Circle

Formulas

Area of a circle: A = πr²

Theorems

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Suitable Grade Level

Grades 6-8