Sure! Let's formulate a problem:
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Problem:
Emily has a circular rug that she wants to place in her living room. The rug has a radius of 2.5 meters. She wants to know the area of the rug in order to ensure it will fit perfectly in the space she has allocated for it.
What is the area of Emily's circular rug?
Solution:
To find the area of a circle, we can use the formula:
[tex]\[ A = \pi r^2 \][/tex]
Where:
- [tex]\( A \)[/tex] is the area
- [tex]\( r \)[/tex] is the radius of the circle
- [tex]\( \pi \)[/tex] (pi) is a constant approximately equal to 3.14159
Given:
- The radius [tex]\( r \)[/tex] is 2.5 meters
Let's calculate the area step-by-step:
1. Square the radius:
[tex]\[ r^2 = (2.5)^2 = 6.25 \][/tex]
2. Multiply the squared radius by [tex]\( \pi \)[/tex]:
[tex]\[ A = \pi \times 6.25 \][/tex]
3. Using the approximate value of [tex]\( \pi \)[/tex]:
[tex]\[ A \approx 3.14159 \times 6.25 \][/tex]
4. Calculate the product:
[tex]\[ A \approx 19.634875 \][/tex]
So, the area of Emily's circular rug is approximately:
[tex]\[ 19.634875 \, \text{square meters} \][/tex]
Therefore, the area of Emily's circular rug is approximately 19.63 square meters.
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This concludes the problem and its detailed, step-by-step solution.
