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

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 2

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

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.