Math Problem Statement

Find the area of a circle with a diameter of 5

Solution

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

Area=πr2\text{Area} = \pi r^2

Where rr is the radius of the circle. The radius is half the diameter, so for a circle with a diameter of 5, the radius rr is:

r=52=2.5r = \frac{5}{2} = 2.5

Now, we substitute r=2.5r = 2.5 into the area formula:

Area=π(2.5)2=π×6.25\text{Area} = \pi (2.5)^2 = \pi \times 6.25

Approximating π\pi as 3.14:

Area3.14×6.25=19.625\text{Area} \approx 3.14 \times 6.25 = 19.625

So, the area of the circle is approximately 19.625 square units.

Would you like more details or have any questions?

Here are some related questions you can explore:

  1. What happens to the area of a circle if the radius is doubled?
  2. How do you find the circumference of a circle if you know the diameter?
  3. What is the relationship between the diameter and the radius of a circle?
  4. How does changing the value of π\pi affect the area of a circle?
  5. Can the formula for the area of a circle be used for ellipses?

Tip: When dealing with circles, it's often easier to work with the radius since the formulas for both area and circumference are based on the radius.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circles
Area of a Circle

Formulas

Area = πr²

Theorems

Area of a circle theorem

Suitable Grade Level

Grades 5-7