Question

Find the surface area of a cylinder with a radius of 5 inches and a height of 10 inches. Use the approximation 3.14 for pi.(1 point)


471 inches
471 inches

471 square inches
471 square inches

345.4 square inches
345.4 square inches

314 square inches

Answer 1

Use the image to answer the question.

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



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

329.7 square yards
329.7 square yards

252.77 square yards
252.77 square yards

252.77 yards
252.77 yards
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Answer 2

To find 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 of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately 3.14.

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

Now, substitute the values into the formula:

1. Calculate the area of the two circular bases:
\[
2\pi r^2 = 2 \times 3.14 \times (5^2) = 2 \times 3.14 \times 25 = 157.0 \text{ square inches}
\]

2. Calculate the area of the curved surface:
\[
2\pi rh = 2 \times 3.14 \times 5 \times 10 = 2 \times 3.14 \times 50 = 314.0 \text{ square inches}
\]

3. Add both areas together:
\[
\text{Surface Area} = 157.0 + 314.0 = 471.0 \text{ square inches}
\]

Thus, the surface area of the cylinder is:

\[
\boxed{471 \text{ square inches}}
\]

Answer 3

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

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

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

Given:
- \( r = 7 \) yards
- \( h = 8 \) yards

Now, substitute the values into the formula:

1. **Calculate the area of the two circular bases:**
\[
2\pi r^2 = 2 \times 3.14 \times (7^2) = 2 \times 3.14 \times 49 = 6.28 \times 49 = 307.72 \text{ square yards}
\]

2. **Calculate the area of the curved surface:**
\[
2\pi rh = 2 \times 3.14 \times 7 \times 8 = 2 \times 3.14 \times 56 = 6.28 \times 56 = 351.68 \text{ square yards}
\]

3. **Add both areas together:**
\[
\text{Surface Area} = 307.72 + 351.68 = 659.4 \text{ square yards}
\]

None of the options given match this calculation, which suggests an error in the calculation of the individual areas. Let's examine the calculations again for accuracy.

### Recalculating Areas

1. **Area of the two circular bases:**
\[
2\pi r^2 = 2 \times 3.14 \times (7^2) = 2 \times 3.14 \times 49 = 307.72 \text{ square yards}
\]

2. **Area of the curved surface (Confirmation):**
\[
2\pi rh = 2 \times 3.14 \times 7 \times 8 = 2 \times 3.14 \times 56 = 6.28 \times 56 = 351.68 \text{ square yards}
\]

3. **Final Calculation of Total Surface Area:**
Now add both calculated areas again:
\[
\text{Surface Area} = 307.72 + 351.68 = 659.4 \text{ square yards}
\]

### Conclusion

The surface area calculation yields approximately **659.4 square yards**, however, this isn't one of the provided responses. Therefore, there may be an inconsistency in the options offered.

To choose the closest answer based on area (but keeping in mind the calculations provided above), **none of the options seem to reflect the computed surface area correctly.**

If we would have to pick an option regardless, it's best to clarify with a precise option or recalculate based on the correct values mentioned.