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:
-
Area of the bases: \[ 2\pi r^2 = 2 \times 3.14 \times (4^2) = 2 \times 3.14 \times 16 = 100.48 , \text{cm}^2 \]
-
Lateral surface area: \[ 2\pi rh = 2 \times 3.14 \times 4 \times 3 = 2 \times 3.14 \times 12 = 75.36 , \text{cm}^2 \]
-
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