To determine the amount of space the circular rug will take up on the floor, you need to find the area of the circle. The area \( A \) of a circle can be calculated using the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.
Since the diameter of the rug is given as 5 feet, the radius \( r \) is half of the diameter:
\[ r = \frac{diameter}{2} = \frac{5 \text{ feet}}{2} = 2.5 \text{ feet} \]
Now, plug the radius into the area formula:
\[ A = \pi (2.5 \text{ feet})^2 \] \[ A = \pi (6.25 \text{ square feet}) \] \[ A \approx 3.14 \times 6.25 \text{ square feet} \approx 19.63 \text{ square feet} \]
Thus, the rug takes up approximately 19.63 square feet of space on the floor.
Final statement:
Finding the area will determine the amount of space the rug takes up on the floor. This can be found by multiplying \( \pi \) times the square of the radius.