A cylinder is labeled with a height of 8 yards and a radius of 7 yards.

Question

Find the surface area of the cylinder. Use the approximation 3.14 for pi.

(1 point)
Responses

329.7 square yards
329.7 square yards

252.77 square yards
252.77 square yards

252.77 yards
252.77 yards

577.76 square yards

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,
• \( h \) is the height,
• \( \pi \) is approximately 3.14.

Given:

• Height \( h = 8 \) yards,
• Radius \( r = 7 \) yards.

Now plug in the values:

\[ \text{Surface Area} = 2 \times 3.14 \times 7 \times (8 + 7) \] \[ = 2 \times 3.14 \times 7 \times 15 \] \[ = 2 \times 3.14 \times 105. \] \[ = 6.28 \times 105. \] \[ = 659.4 \text{ square yards}. \]

So upon re-evaluation, it looks like I made a mistake in calculation.

Let's double-check the formula.

\[ = 2 \times 3.14 \times 7 \times 15 \] First, calculate \( 2 \times 3.14 \):

\[ = 6.28 \]

Next, multiply \( 6.28 \times 105 \):

\[ = 659.4 \]

So the correct calculation shows the surface area of the cylinder is indeed 659.4 square yards.

However, regarding the choices given:

• 329.7 square yards
• 252.77 square yards
• 252.77 yards
• 577.76 square yards

None of these options match the calculated surface area; the answer is 659.4 square yards.

Thus, I believe there may have been a mistake in the answer choices provided.

Answer 2

Wrong

Answer 3

Let's re-calculate the surface area of the cylinder step by step to ensure accuracy.

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

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

Where:

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

Given:

• Radius \( r = 7 \) yards,
• Height \( h = 8 \) yards.

Now let's substitute these values into the formula:

1. Calculate \( h + r \): \[ h + r = 8 + 7 = 15 \]

2. Now substitute into the surface area formula: \[ A = 2 \times 3.14 \times 7 \times 15 \]

3. First calculate \( 2 \times 3.14 \): \[ 2 \times 3.14 = 6.28 \]

4. Now multiply \( 6.28 \) by \( 7 \): \[ 6.28 \times 7 = 43.96 \]

5. Finally, multiply \( 43.96 \) by \( 15 \): \[ 43.96 \times 15 = 659.4 \]

Upon reevaluation, it seems I was correct that the surface area calculation yields 659.4 square yards. However, if there is a misunderstanding regarding the options or the dimensions provided, I encourage you to verify that the values for radius and height are correct.

If those values are indeed confirmed (7 yards radius and 8 yards height), the calculation stands at 659.4 square yards.

If there's any specific reasoning or instruction you're following, please provide more details so I can assist properly!