Question

A cylinder is labeled with a height of 3 yards and a radius of 2 yards. Find the surface area of the cylinder. Use the approximation of 3.14 for pi. (1 point) Responses 75.36 75.36 25.12 25.12 62.8 62.8 32.97

Answer 1

the answer is 1 of the 4 options.
75.36
25.12
62.8
32.97

Answer 2

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 and \( h \) is the height of the cylinder.

Given:
- \( h = 3 \) yards
- \( r = 2 \) yards
- \( \pi \approx 3.14 \)

Now, let's plug in the values:

1. Calculate \( h + r \):
\[
h + r = 3 + 2 = 5 \text{ yards}
\]

2. Calculate the surface area:
\[
\text{Surface Area} = 2 \times 3.14 \times 2 \times 5
\]

First calculate \( 2 \times 2 \times 5 \):
\[
2 \times 2 = 4
\]
\[
4 \times 5 = 20
\]

Now multiply by \( 2 \times 3.14 \):
\[
2 \times 3.14 = 6.28
\]

Now multiply \( 6.28 \) by \( 20 \):
\[
6.28 \times 20 = 125.6
\]

Thus, the surface area of the cylinder is \( 125.6 \) square yards.

Since none of the provided multiple-choice responses matches the correct surface area, there seems to be an error either in the options or in the given problem. Please double-check the options or the input values.

Answer 3

Let's re-evaluate the calculations for the surface area of the cylinder using the given options.

The formula for the surface area \( A \) of a cylinder is:

\[
A = 2\pi r(h + r)
\]

Given:
- Height \( h = 3 \) yards
- Radius \( r = 2 \) yards
- Using \( \pi \approx 3.14 \)

First, calculate \( h + r \):

\[
h + r = 3 + 2 = 5 \text{ yards}
\]

Now substitute the values into the surface area formula:

\[
A = 2 \times 3.14 \times 2 \times 5
\]

Calculating step by step:

1. Calculate \( 2 \times 2 \):
\[
2 \times 2 = 4
\]
2. Now multiply by \( 5 \):
\[
4 \times 5 = 20
\]
3. Multiply by \( 2\pi \) (where \( \pi \approx 3.14 \)):
\[
2 \times 3.14 = 6.28
\]
4. Now multiply \( 6.28 \) by \( 20 \):
\[
6.28 \times 20 = 125.6
\]

So, I calculated the surface area as \( 125.6 \) square yards, which does not align with the options provided.

Let's double-check the cylinder's surface area formula to ensure we're not missing anything. The full surface area \( A \) can also be calculated as:

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

Where:
- \( 2\pi r^2 \) is the area of the top and bottom circles,
- \( 2\pi rh \) is the lateral surface area.

Calculating each part:

1. Area of the top and bottom:
\[
2\pi r^2 = 2 \times 3.14 \times (2^2) = 2 \times 3.14 \times 4 = 25.12
\]

2. Lateral surface area:
\[
2\pi rh = 2 \times 3.14 \times 2 \times 3 = 2 \times 3.14 \times 6 = 37.68
\]

Add both areas together:

\[
A = 25.12 + 37.68 = 62.8
\]

Thus, the surface area of the cylinder is \( 62.8 \) square yards.

The correct option from the choices provided is:

**62.8**.