A pizza restaurant uses special placemats for birthday parties. The happy face on the mat has a diameter measuring 20 centimeters. Determine the area of the happy face to the neare... A pizza restaurant uses special placemats for birthday parties. The happy face on the mat has a diameter measuring 20 centimeters. Determine the area of the happy face to the nearest square centimeter.
Understand the Problem
The question is asking us to calculate the area of a circle, given the diameter of 20 centimeters. We will use the formula for the area of a circle, A = πr², where r is the radius. The radius can be found by dividing the diameter by 2.
Answer
$314 \, \text{cm}^2$
Answer for screen readers
The area of the happy face is approximately $314 , \text{cm}^2$.
Steps to Solve
- Calculate the radius To find the radius, divide the diameter by 2. Given that the diameter is 20 cm:
$$ r = \frac{20 , \text{cm}}{2} = 10 , \text{cm} $$
- Use the area formula The formula for the area of a circle is:
$$ A = \pi r^2 $$
Substituting the value of the radius:
$$ A = \pi (10 , \text{cm})^2 $$
- Calculate the area Calculate the square of the radius:
$$ A = \pi (100 , \text{cm}^2) $$
Now, using the approximate value of $\pi \approx 3.14$:
$$ A \approx 3.14 \times 100 , \text{cm}^2 = 314 , \text{cm}^2 $$
The area of the happy face is approximately $314 , \text{cm}^2$.
More Information
The area of a circle increases rapidly with the radius. In this case, a small change in the radius can significantly affect the area, demonstrating the power of exponential growth.
Tips
- Forgetting to divide the diameter by 2 to find the radius.
- Using an incorrect value for $\pi$. Always use approximately 3.14 or $\pi$ on a calculator.
- Confusing area with circumference. Remember that area is measured in square units.
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