Question

A large cylinder-shaped cushion has a height of 1 foot and a diameter of 4 feet. How many square feet of fabric will be need to reupholster the entire cushion? Use 3.14 for pi.(1 point)
Responses

37.68 square feet
37.68 square feet

125.6 square feet
125.6 square feet

12.56 square feet
12.56 square feet

25.12 square feet

Answer 1

To find the amount of fabric needed to reupholster the entire cylinder-shaped cushion, we need to calculate the surface area of the cylinder.

A cylinder's surface area consists of the lateral (side) area and the area of the two circular bases. The formulas we use are:

- Lateral area: \(A_{\text{lateral}} = 2\pi rh\)
- Area of the two bases: \(A_{\text{bases}} = 2\pi r^2\)

Where:
- \(r\) is the radius
- \(h\) is the height

Given:
- Height \(h = 1\) foot
- Diameter = 4 feet, so radius \(r = \frac{4}{2} = 2\) feet

**1. Calculate the lateral area:**
\[
A_{\text{lateral}} = 2\pi rh = 2 \times 3.14 \times 2 \times 1
\]
\[
= 2 \times 3.14 \times 2 = 12.56 \text{ square feet}
\]

**2. Calculate the area of the two bases:**
\[
A_{\text{bases}} = 2\pi r^2 = 2 \times 3.14 \times (2^2)
\]
\[
= 2 \times 3.14 \times 4 = 25.12 \text{ square feet}
\]

**3. Calculate the total surface area:**
\[
A_{\text{total}} = A_{\text{lateral}} + A_{\text{bases}} = 12.56 + 25.12
\]
\[
= 37.68 \text{ square feet}
\]

Thus, the total amount of fabric needed to reupholster the entire cushion is **37.68 square feet**.

So the correct response is:
**37.68 square feet**.