Question

Find the surface area of a cylinder with a radius of 5 inches and a height of 10 inches u=Use the aproximation 3.14 as pi.

Answer 1

you sure-?

Answer 2

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, and
- \( \pi \) is approximately \( 3.14 \).

Given:
- \( r = 5 \) inches,
- \( h = 10 \) inches.

Now plug these values into the formula:

\[
\text{Surface Area} = 2 \times 3.14 \times 5 (10 + 5)
\]

Calculating \( h + r \):

\[
h + r = 10 + 5 = 15
\]

Now substitute this back into the formula:

\[
\text{Surface Area} = 2 \times 3.14 \times 5 \times 15
\]

Calculating:

1. First calculate \( 2 \times 3.14 = 6.28 \).
2. Then calculate \( 5 \times 15 = 75 \).
3. Finally, multiply these results together:

\[
\text{Surface Area} = 6.28 \times 75
\]

Calculating \( 6.28 \times 75 \):

\[
6.28 \times 75 = 471
\]

Thus, the surface area of the cylinder is approximately:

\[
\text{Surface Area} \approx 471 \text{ square inches}
\]

Answer 3

Let’s verify the calculations step by step for the surface area of the cylinder to ensure everything is correct.

The formula for the surface area of a cylinder is:

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

where:
- \( r = 5 \) inches (radius),
- \( h = 10 \) inches (height),
- \( \pi \approx 3.14 \).

**Step 1: Calculate \( h + r \)**

\[
h + r = 10 + 5 = 15
\]

**Step 2: Plug the values into the formula**

\[
\text{Surface Area} = 2 \times 3.14 \times 5 \times 15
\]

**Step 3: Calculate \( 2 \times 3.14 \)**

\[
2 \times 3.14 = 6.28
\]

**Step 4: Calculate \( 5 \times 15 \)**

\[
5 \times 15 = 75
\]

**Step 5: Now multiply \( 6.28 \times 75 \)**

Now let's calculate \( 6.28 \times 75 \):

\[
6.28 \times 75 = 471
\]

### Conclusion

After verifying the calculations, the surface area of the cylinder is indeed approximately:

\[
\text{Surface Area} \approx 471 \text{ square inches}
\]

If you have any further questions or need additional clarification, feel free to ask!