Question

A circular piece of fabric has a radius of 1.2 ft. The fabric sells for $5.40 per ft².

What is the total cost of the circular piece of fabric?

Use 3.14 for pi.
Responses

$6.48
$6.48

$20.35
$20.35

$24.42
$24.42

$40.69
$40.69

Answer 1

To find the total cost of the circular piece of fabric, we first need to calculate its area using the formula for the area of a circle:

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

Given:
- Radius \( r = 1.2 \) ft
- Using \( \pi \approx 3.14 \)

Substituting the values into the formula gives:

\[
\text{Area} = 3.14 \times (1.2)^2
\]

Calculating \( (1.2)^2 \):

\[
(1.2)^2 = 1.44
\]

Now, substituting back into the area formula:

\[
\text{Area} = 3.14 \times 1.44 = 4.5136 \text{ ft}^2
\]

Next, we calculate the cost of the fabric. The cost per square foot is given as $5.40. Therefore, the total cost \( C \) can be calculated as follows:

\[
C = \text{Area} \times \text{Cost per ft}^2
\]
\[
C = 4.5136 \text{ ft}^2 \times 5.40 \text{ dollars/ft}^2
\]
\[
C = 24.42624 \text{ dollars}
\]

Rounding to two decimal places, the total cost is:

\[
C \approx 24.43 \text{ dollars}
\]

Looking at the given responses, the closest matching answer is:

**$24.42**