To find the surface area of a right circular cylinder, we use the formula:
\[ SA = 2\pi r(h + r) \]
where \( r \) is the radius and \( h \) is the height of the cylinder.
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Find the radius: The diameter of the cylinder is 8 feet, so the radius \( r \) is half of the diameter: \[ r = \frac{8}{2} = 4 \text{ feet} \]
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Substitute the values into the surface area formula: Given that \( h = 21.5 \) feet and using \( \pi \approx 3.14 \): \[ SA = 2 \times 3.14 \times 4 \times (21.5 + 4) \]
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Calculate \( h + r \): \[ h + r = 21.5 + 4 = 25.5 \]
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Calculate the surface area: Now plug this value back into the surface area formula: \[ SA = 2 \times 3.14 \times 4 \times 25.5 \]
First, calculate \( 2 \times 3.14 \times 4 \): \[ 2 \times 3.14 = 6.28 \] \[ 6.28 \times 4 = 25.12 \]
Now multiply by \( 25.5 \): \[ SA = 25.12 \times 25.5 \]
Calculate \( 25.12 \times 25.5 \): \[ SA \approx 640.56 \]
Thus, the surface area of the water tank is approximately \( 640.56 \) square feet.