Question

what is the surface area of this cylinder use pi = 3.14 and round you're answer to the nearest hundredth the radius is radius = 1 /2 × diameter = 1/ 2 × 19= 9.5 and the height is 4.9 yd

Answer 1

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

\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh
\]

Where:
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is approximately \( 3.14 \).

First, let's verify the radius you provided:
- The diameter is 19, so the radius \( r \) is:

\[
r = \frac{1}{2} \times 19 = 9.5 \, \text{yd}
\]

The height \( h \) is given as:

\[
h = 4.9 \, \text{yd}
\]

Now we can plug these values into the surface area formula.

1. Calculate the first part \( 2\pi r^2 \):

\[
2\pi r^2 = 2 \times 3.14 \times (9.5)^2
\]
\[
(9.5)^2 = 90.25
\]
\[
2 \times 3.14 \times 90.25 = 565.005
\]

2. Calculate the second part \( 2\pi rh \):

\[
2\pi rh = 2 \times 3.14 \times 9.5 \times 4.9
\]
\[
2 \times 3.14 \times 9.5 = 59.24
\]
\[
59.24 \times 4.9 = 290.976
\]

3. Add both parts together to find the total surface area:

\[
\text{Surface Area} = 565.005 + 290.976 = 855.981
\]

Finally, rounding to the nearest hundredth, the surface area of the cylinder is:

\[
\boxed{855.98} \, \text{yd}^2
\]