Question

Azul wants to change the fabric of a cylinder-shaped ottoman. The cushion has a height of 2 feet and a radius of 3.5 feet.

How much fabric is needed to cover the entire cushion of the ottoman?

Use 3.14 for pi (𝜋).



Formula for surface area of a cylinder: SA = 2𝜋r 2
+ 2𝜋rℎ

(1 point)
Responses

120.89 ft2
120.89 ft2

76.93 ft2
76.93 ft2

43.96 ft2
43.96 ft2

105.98 ft2
105.98 ft2
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Answer 1

To find the amount of fabric needed to cover the entire cushion of the cylindrical ottoman, we will use the formula for the surface area of a cylinder:

\[
SA = 2\pi r^2 + 2\pi rh
\]

Where:
- \( r \) is the radius
- \( h \) is the height
- \( \pi \) is approximately 3.14

Given:
- \( r = 3.5 \) feet
- \( h = 2 \) feet

Now, substituting the values into the formula:

1. Calculate the area of the top and bottom (circular) surfaces:
\[
2\pi r^2 = 2 \times 3.14 \times (3.5)^2
\]
First, calculate \( (3.5)^2 \):
\[
(3.5)^2 = 12.25
\]
Now plug that back into the equation:
\[
2 \times 3.14 \times 12.25 = 76.93 \, \text{ft}^2
\]

2. Calculate the lateral surface area:
\[
2\pi rh = 2 \times 3.14 \times 3.5 \times 2
\]
Calculate \( 3.5 \times 2 = 7 \):
\[
2 \times 3.14 \times 7 = 43.96 \, \text{ft}^2
\]

3. Now add both areas together to find the total surface area:
\[
SA = 76.93 + 43.96 = 120.89 \, \text{ft}^2
\]

Therefore, the total fabric needed to cover the entire cushion of the ottoman is **120.89 ft²**.