To calculate the surface area \( A \) of a cylinder, you can use the formula:
\[ A = 2\pi r(h + r) \]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.
In this case, you provided dimensions of 10 ft for both the height and the diameter. To find the radius, we divide the diameter by 2:
\[ r = \frac{10 \text{ ft}}{2} = 5 \text{ ft} \]
Now, we can plug the values into the surface area formula:
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Calculate \( h + r \): \[ h + r = 10 \text{ ft} + 5 \text{ ft} = 15 \text{ ft} \]
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Substitute \( r \) and \( h + r \) into the surface area formula: \[ A = 2 \pi r (h + r) = 2 \times 3.14 \times 5 \text{ ft} \times 15 \text{ ft} \]
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First, calculate \( 2 \times 3.14 \times 5 \): \[ 2 \times 3.14 = 6.28 \] \[ 6.28 \times 5 = 31.4 \]
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Now multiply by \( 15 \): \[ A = 31.4 \times 15 = 471 \]
Thus, the surface area of the cylinder is:
\[ A = 471 \text{ ft}^2 \]
Since the question asks to round to the nearest hundredth, the answer is:
\[ \text{Surface Area} \approx 471.00 \text{ ft}^2 \]