Cones, Cylinders, & Spheres Online Practice

Question

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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

25.12 square feet
25.12 square feet

125.6 square feet
125.6 square feet

12.56 square feet

Answer 1

To find the surface area of a cylinder, you can use the formula:

\[ \text{Surface Area} = 2\pi r(h + r) \]

where:

• \( r \) is the radius of the base of the cylinder,
• \( h \) is the height of the cylinder,
• \( \pi \) is approximately 3.14.

The cylinder has a diameter of 4 feet, which means the radius \( r \) is half of that:

\[ r = \frac{4}{2} = 2 \text{ feet} \]

The height \( h \) is given as 1 foot. Now we can plug the values into the formula:

\[ \text{Surface Area} = 2 \times 3.14 \times 2 \times (1 + 2) \]

Calculating it step-by-step:

1. Calculate \( (h + r) \):

   \( h + r = 1 + 2 = 3 \)

2. Substitute into the surface area formula:

   \[ \text{Surface Area} = 2 \times 3.14 \times 2 \times 3 \]

3. Calculate:

   • \( 2 \times 2 = 4 \)
   • \( 4 \times 3 = 12 \)
   • \( 12 \times 3.14 = 37.68 \)

So, the total surface area is 37.68 square feet.

Therefore, the answer is:

37.68 square feet