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 15.7 ft² in floorspace.
The rug will take up 15.7 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 78.5 ft² in floorspace.
The rug will take up 78.5 ft² in floorspace.

Answer 1

To find the area of a circular rug, you can use the formula:

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

where \( r \) is the radius of the circle. Since the diameter of the rug is 5 feet, we can find the radius by dividing the diameter by 2:

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

Now, substituting the radius into the area formula:

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

Calculating \( (2.5)^2 \):

\[
(2.5)^2 = 6.25
\]

Now substitute back into the area formula:

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

Rounding to one decimal place, the area is approximately:

\[
\text{Area} \approx 19.6 \text{ ft}^2
\]

Therefore, the rug will take up **19.6 ft²** in floorspace.