Question

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2cm and 5 cm
Question
Find the surface area of a cylinder with a radius of 4 and a height of 3. Use 3.14 for π
.

Round your answer to the nearest tenths place.



(1 point)
Responses

87.9 cm2
87.9 cm 2

175.8 cm2
175.8 cm 2

120.3 cm2
120.3 cm 2

75.3 cm2

Answer 1

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

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

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

Given:
- Radius (\( r \)) = 4 cm
- Height (\( h \)) = 3 cm

Let's plug the values into the formula:

\[
\text{Surface Area} = 2 \times 3.14 \times 4 \times (3 + 4)
\]
\[
= 2 \times 3.14 \times 4 \times 7
\]
\[
= 2 \times 3.14 \times 28
\]
\[
= 6.28 \times 28
\]
\[
= 176.84
\]

Now rounding to the nearest tenths place:

\[
176.84 \approx 176.8 \, \text{cm}^2
\]

However, since this value does not match any of the provided responses, let’s double-check through calculating the total surface area of the cylinder, which also involves the areas of the two circular bases.

The total surface area formula also can be split into:

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

Calculating each part:

1. **Area of the bases**:
\[
2\pi r^2 = 2 \times 3.14 \times (4^2) = 2 \times 3.14 \times 16 = 100.48 \, \text{cm}^2
\]

2. **Lateral surface area**:
\[
2\pi rh = 2 \times 3.14 \times 4 \times 3 = 2 \times 3.14 \times 12 = 75.36 \, \text{cm}^2
\]

3. **Total surface area**:
Combining both parts:
\[
100.48 + 75.36 = 175.84 \, \text{cm}^2
\]

Rounding this to the nearest tenths place gives:

\[
175.8 \, \text{cm}^2
\]

So, the correct response is:

**175.8 cm²**