Math Problem Statement

Find the area of the circle to the nearest whole square foot. Use 3.14 as an approximation for π.

Solution

To solve the problem of finding the area of the circle, we can use the formula for the area of a circle:

Area=π×r2\text{Area} = \pi \times r^2

Here, rr is the radius of the circle, and π\pi is given as 3.14. According to the image, the diameter of the circle is 8 feet, so the radius rr is half of the diameter:

r=82=4 feetr = \frac{8}{2} = 4 \text{ feet}

Now, substitute the values into the area formula:

Area=3.14×(4)2=3.14×16=50.24 square feet\text{Area} = 3.14 \times (4)^2 = 3.14 \times 16 = 50.24 \text{ square feet}

Rounding 50.24 to the nearest whole number, we get:

Area50 square feet\text{Area} \approx 50 \text{ square feet}

So, the area of the circle is 50 square feet.

Would you like any more details or have any questions? Here are some related questions for further exploration:

  1. How would the area change if the diameter was doubled?
  2. What would the area be if π\pi were approximated as 22/7 instead of 3.14?
  3. How would you calculate the circumference of this circle?
  4. If the circle’s diameter was given in inches instead of feet, how would the calculation change?
  5. How do you find the area of a sector of a circle given the central angle?

Tip: Always remember that the radius is half the diameter when calculating the area of a circle.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area of a Circle

Formulas

Area = π × r^2

Theorems

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Suitable Grade Level

Grades 6-8