To find the total volume of the semi-sphere sitting on top of the cylinder, we need to calculate the volume of both shapes and then add them together.
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Volume of the Cylinder: The formula for the volume \( V \) of a cylinder is given by: \[ V_{\text{cylinder}} = \pi r^2 h \] where \( r \) is the radius and \( h \) is the height of the cylinder.
The diameter of the cylinder is 38 feet, so the radius \( r \) is: \[ r = \frac{38}{2} = 19 \text{ feet} \]
The height \( h \) of the cylinder is 35 feet. Plugging in the values: \[ V_{\text{cylinder}} = 3.14 \times (19)^2 \times 35 \]
First, calculate \( (19)^2 \): \[ (19)^2 = 361 \]
Now, substitute that back into the cylinder volume formula: \[ V_{\text{cylinder}} = 3.14 \times 361 \times 35 \] Calculate \( 361 \times 35 \): \[ 361 \times 35 = 12635 \]
Now multiply by \( 3.14 \): \[ V_{\text{cylinder}} = 3.14 \times 12635 \approx 39644.9 \text{ cubic feet} \]
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Volume of the Semi-Sphere: The formula for the volume \( V \) of a sphere is: \[ V_{\text{sphere}} = \frac{4}{3} \pi r^3 \]
Hence, the volume of a semi-sphere is half of that: \[ V_{\text{semi-sphere}} = \frac{1}{2} \times \frac{4}{3} \pi r^3 = \frac{2}{3} \pi r^3 \]
Using the radius \( r = 19 \) feet: \[ V_{\text{semi-sphere}} = \frac{2}{3} \times 3.14 \times (19)^3 \]
Calculate \( (19)^3 \): \[ (19)^3 = 6859 \]
Now substitute back into the semi-sphere volume formula: \[ V_{\text{semi-sphere}} = \frac{2}{3} \times 3.14 \times 6859 \]
First, calculate \( 3.14 \times 6859 \): \[ 3.14 \times 6859 \approx 21501.46 \]
Now apply \( \frac{2}{3} \): \[ V_{\text{semi-sphere}} = \frac{2}{3} \times 21501.46 \approx 14334.31 \text{ cubic feet} \]
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Total Volume: Now we can add the volumes of the cylinder and the semi-sphere: \[ V_{\text{total}} = V_{\text{cylinder}} + V_{\text{semi-sphere}} \approx 39644.9 + 14334.31 \approx 53979.21 \text{ cubic feet} \]
Finally, rounding to the nearest whole number, the total volume is: \[ \boxed{53979} \text{ cubic feet} \]