What is the area of the trampoline mat to the nearest square foot?
Understand the Problem
The question is asking for the area of a circular trampoline mat with a given diameter of 18 feet. To find the area, we will use the formula for the area of a circle, A = πr², where r is the radius (half of the diameter).
Answer
The area of the trampoline mat is approximately $254$ square feet.
Answer for screen readers
The area of the trampoline mat is approximately $254$ square feet.
Steps to Solve
- Calculate the Radius
The radius ( r ) is half of the diameter. Given that the diameter is 18 feet: $$ r = \frac{18}{2} = 9 \text{ feet} $$
- Use the Area Formula
We will now use the area formula for a circle, which is: $$ A = \pi r^2 $$
Substituting the radius into the formula: $$ A = \pi (9)^2 $$
- Calculate the Area
Calculating ( 9^2 ): $$ 9^2 = 81 $$
Now plug this value back into the area formula: $$ A = \pi \times 81 $$
- Compute the Value of the Area
Using ( \pi \approx 3.14 ): $$ A \approx 3.14 \times 81 \approx 254.34 $$
- Round to the Nearest Square Foot
Rounding ( 254.34 ) to the nearest whole number gives: $$ A \approx 254 \text{ square feet} $$
The area of the trampoline mat is approximately $254$ square feet.
More Information
The area of a circle increases with the square of the radius, which is why small increases in diameter lead to much larger increases in area. This concept is crucial in various applications, from gardening to architecture.
Tips
- Forgetting to convert the diameter to radius: Remember that the radius is half of the diameter.
- Not using the correct value of ( \pi ): While ( \pi ) can be approximated as 3.14, using its full value (3.14159...) will yield a more precise result.
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