Question

Diameter is 7
height is 8
Find the surface area of the cylinder. Use the approximation 3.14 for pi.

(1 point)
Responses

577.76 square yards
577.76 square yards

252.77 square yards
252.77 square yards

329.7 square yards
329.7 square yards

252.77 yards

Answer 1

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

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

where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.

Given that the diameter of the cylinder is 7, the radius \( r \) is half of that:

\[ r = \frac{7}{2} = 3.5 \]

The height \( h \) is given as 8.

Now, substitute the values into the formula:

\[ \text{Surface Area} = 2 \times 3.14 \times 3.5 \times (8 + 3.5) \]

Calculate \( h + r \):

\[ h + r = 8 + 3.5 = 11.5 \]

Now substitute this back into the formula:

\[ \text{Surface Area} = 2 \times 3.14 \times 3.5 \times 11.5 \]

Calculate it step by step:

1. Calculate \( 2 \times 3.14 = 6.28 \)
2. Calculate \( 3.5 \times 11.5 = 40.25 \)
3. Finally calculate \( 6.28 \times 40.25 \)

\[ 6.28 \times 40.25 \approx 252.77 \]

Thus, the surface area of the cylinder is approximately:

**252.77 square yards**.