Math Problem Statement

What is the area of a circle if the radius is 5?

Solution

To calculate the area of a circle, we use the formula:

A=πr2A = \pi r^2

Where:

  • AA is the area,
  • π\pi is approximately 3.14159,
  • rr is the radius.

Given that the radius r=5r = 5, we can substitute this value into the formula:

A=π×(5)2=π×253.14159×2578.54A = \pi \times (5)^2 = \pi \times 25 \approx 3.14159 \times 25 \approx 78.54

Thus, the area of the circle is approximately 78.54 square units.

Would you like further details on this? Let me know if you have any questions!

Here are some related questions:

  1. How does changing the radius affect the area of a circle?
  2. What would the area be if the radius were doubled?
  3. How is the circumference of a circle related to the radius?
  4. What is the area of a circle with a radius of 10?
  5. How can the area formula for a circle be derived from geometry?

Tip: Remember that the area grows quadratically with the radius. Doubling the radius will quadruple the area!

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Math Problem Analysis

Mathematical Concepts

Geometry
Circles
Area

Formulas

A = πr^2

Theorems

Area of a circle

Suitable Grade Level

Grades 5-7