To find the surface area of a cylinder, you can use the following 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
Given that the diameter of the cylinder is 5 cm, we can find the radius:
\[ r = \frac{\text{diameter}}{2} = \frac{5}{2} = 2.5 \text{ cm} \]
The height \( h \) is given as 15 cm.
Now we can plug these values into the formula for surface area:
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Calculate the area of the bases (top and bottom): \[ 2\pi r^2 = 2\pi(2.5)^2 = 2\pi(6.25) = 12.5\pi \]
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Calculate the lateral surface area: \[ 2\pi rh = 2\pi(2.5)(15) = 75\pi \]
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Adding both parts together: \[ \text{Surface Area} = 12.5\pi + 75\pi = 87.5\pi \]
Now calculate the numerical value of \( 87.5\pi \): Using \( \pi \approx 3.14 \):
\[ 87.5 \times 3.14 \approx 274.75 \]
Rounding to the nearest whole number, we find:
\[ \text{Surface Area} \approx 275 \text{ square centimeters} \]
However, none of the options you provided match this result exactly. The closest option based on approximate values would be useful to check what each option corresponds to using a more accurate value for \( \pi \).
If you use \( \pi \approx 3.14159 \): \[ 87.5 \times 3.14159 \approx 274.887 \] Rounding this gives you 275.
If you require an approximate check with provided options after calculating numeric values based on \( \pi \). The surface area of this cylinder is approximately 275 square centimeters.