Question
Maria bought a circular rug to go in her bedroom. It has a diameter of 5 feet. How much space will the rug take up on the floor?
(2 points)
Finding the
will determine the amount of space the rug takes up on the floor. This can be found by multiplying π
times
.
(2 points)
Finding the
will determine the amount of space the rug takes up on the floor. This can be found by multiplying π
times
.
Answers
GPT-4o mini
To determine the amount of space the circular rug takes up on the floor, we need to calculate its area. The area \( A \) of a circle can be found using the formula:
\[
A = \pi r^2
\]
where \( r \) is the radius of the circle.
Given that the rug has a diameter of 5 feet, we first find the radius by dividing the diameter by 2:
\[
r = \frac{5 \text{ feet}}{2} = 2.5 \text{ feet}
\]
Next, we can substitute the radius into the area formula:
\[
A = \pi (2.5 \text{ feet})^2
\]
\[
A = \pi (6.25 \text{ square feet})
\]
\[
A \approx 3.14 \times 6.25 \text{ square feet} \approx 19.63 \text{ square feet}
\]
So, the rug will take up approximately **19.63 square feet** of space on the floor.
\[
A = \pi r^2
\]
where \( r \) is the radius of the circle.
Given that the rug has a diameter of 5 feet, we first find the radius by dividing the diameter by 2:
\[
r = \frac{5 \text{ feet}}{2} = 2.5 \text{ feet}
\]
Next, we can substitute the radius into the area formula:
\[
A = \pi (2.5 \text{ feet})^2
\]
\[
A = \pi (6.25 \text{ square feet})
\]
\[
A \approx 3.14 \times 6.25 \text{ square feet} \approx 19.63 \text{ square feet}
\]
So, the rug will take up approximately **19.63 square feet** of space on the floor.