Question

Maria bought a circular rug to go in her bedroom. It has a diameter of 5 feet. How much floor space will the rug take up?





Use 3.14 for π

(1 point)
Responses

The rug will take up 31.4 ft² in floorspace.
The rug will take up 31.4 ft² in floorspace.

The rug will take up 78.5 ft² in floorspace.
The rug will take up 78.5 ft² in floorspace.

The rug will take up 19.6 ft² in floorspace.
The rug will take up 19.6 ft² in floorspace.

The rug will take up 15.7 ft² in floorspace.

Answer 1

To find the floor space (area) that the rug takes up, we use the formula for the area of a circle:

\[
\text{Area} = \pi r^2
\]

Where \( r \) is the radius of the circle. The radius is half of the diameter. Since the diameter of the rug is 5 feet, the radius \( r \) is:

\[
r = \frac{5}{2} = 2.5 \text{ feet}
\]

Now, plug the radius into the area formula using \( \pi \approx 3.14 \):

\[
\text{Area} = 3.14 \times (2.5)^2
\]

First, calculate \( (2.5)^2 \):

\[
(2.5)^2 = 6.25
\]

Now, calculate the area:

\[
\text{Area} = 3.14 \times 6.25 = 19.625
\]

Rounding this to one decimal place gives us 19.6 ft².

Therefore, the correct response is:

**The rug will take up 19.6 ft² in floorspace.**