Math Problem Statement

Find the area of a circle with a radius of 5

Solution

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

A=πr2A = \pi r^2

Where:

  • AA is the area of the circle
  • rr is the radius of the circle
  • π\pi is approximately 3.14159

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

A=π(5)2=π×253.14159×25=78.53975A = \pi (5)^2 = \pi \times 25 \approx 3.14159 \times 25 = 78.53975

So, the area of the circle is approximately:

A78.54square unitsA \approx 78.54 \, \text{square units}

Would you like further details or explanations on this?

Related questions:

  1. How do you find the circumference of a circle?
  2. What happens to the area of a circle if the radius is doubled?
  3. How is the area of a circle related to the diameter?
  4. How would you calculate the area of a sector of a circle?
  5. How can you derive the formula for the area of a circle using integration?

Tip: Always remember that the area of a circle grows quadratically with the radius, meaning that if you double the radius, the area will increase by a factor of four.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circle Area
Pi
Exponents

Formulas

A = πr^2

Theorems

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Suitable Grade Level

Grades 6-8