Math Problem Statement

Find the area of a circle with a diameter of 20 feet using π = 3.14.

Solution

The problem asks to find the area of a circle with a diameter of 20 feet, using π=3.14\pi = 3.14.

The formula for the area AA of a circle is: A=πr2A = \pi r^2 where rr is the radius. Since the diameter is given as 20 feet, the radius rr is half of the diameter: r=202=10ftr = \frac{20}{2} = 10 \, \text{ft}

Now, we can calculate the area: A=3.14×102=3.14×100=314ft2A = 3.14 \times 10^2 = 3.14 \times 100 = 314 \, \text{ft}^2

So, the area of the circle is 314 square feet.

Would you like more details or have any questions about this solution?

Here are 5 related questions you might find interesting:

  1. How would the area change if the diameter were doubled?
  2. What is the circumference of this circle?
  3. How can we calculate the volume if this circle was part of a sphere?
  4. What happens to the area if π\pi is approximated as 3.1416 instead of 3.14?
  5. Can you derive the area formula from the definition of π\pi?

Tip: Always remember that the radius is half of the diameter, which is key in many circle-related problems!

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Math Problem Analysis

Mathematical Concepts

Geometry
Circle Area

Formulas

A = πr²

Theorems

Area of a Circle

Suitable Grade Level

Grades 6-8