Question

For this cylinder the radius r = 6.8 inches and the height L = 14.2 inches. Which is the BEST estimate for the surface area? (Use π = 3.14)

Answer 1

To find the surface area \( S \) of a cylinder, you can use the formula:

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

where:
- \( r \) is the radius
- \( h \) is the height

Given:
- Radius \( r = 6.8 \) inches
- Height \( h = 14.2 \) inches
- Use \( \pi \approx 3.14 \)

First, we calculate \( h + r \):

\[
h + r = 14.2 + 6.8 = 21.0 \text{ inches}
\]

Now, substitute \( r \) and \( h + r \) into the surface area formula:

\[
S = 2 \times 3.14 \times 6.8 \times 21.0
\]

Now calculate \( 2 \times 3.14 \):

\[
2 \times 3.14 = 6.28
\]

Now multiply this by \( 6.8 \):

\[
6.28 \times 6.8 = 42.784
\]

Finally, multiply that result by \( 21.0 \):

\[
42.784 \times 21.0 \approx 897.424
\]

Therefore, the BEST estimate for the surface area of the cylinder is approximately \( 897.42 \) square inches. If we round to the nearest whole number, we can estimate it as:

\[
\text{Surface Area } \approx 897 \text{ square inches}
\]