To find the volume of the cylinder, we can follow these steps:
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Calculate the base area of the cylinder: The base area \( B \) of a cylinder is given by the formula for the area of a circle, \( B = \pi r^2 \), where \( r \) is the radius of the base. In this case, the radius given is 5 ft.
\[ B = \pi (5)^2 = \pi (25) = 25\pi , \text{ft}^2 \]
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Multiply the base area by the height: The height \( H \) of the cylinder is 3 ft. The volume \( V \) is calculated as:
\[ V = B \cdot H = 25\pi \cdot 3 \]
Now, multiply \( 25 \) by \( 3 \):
\[ 25 \cdot 3 = 75 \]
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Substitute back into the volume formula:
\[ V = 75\pi , \text{ft}^3 \]
So the volume of the cylinder is:
\[ V = 75\pi , \text{ft}^3 \]
If you need a numerical approximation, using \( \pi \approx 3.14 \):
\[ V \approx 75 \cdot 3.14 \approx 235.5 , \text{ft}^3 \]
Therefore, the final answer for the volume is:
\[ V = 75\pi , \text{ft}^3 \quad \text{or approximately} \quad 235.5 , \text{ft}^3 \]