What is the weight of a cylinder made of solid aluminum with a diameter of 4 feet and a height of 5 feet, if its unit weight is 165 pounds per cubic foot?

To determine the weight of a solid aluminum cylinder, we first need to calculate the volume of the cylinder, and then multiply that volume by the unit weight of aluminum.

The formula for the volume ( V ) of a cylinder is given by:

[ V = \pi r^2 h ]

where ( r ) is the radius and ( h ) is the height. Since the diameter of the cylinder is 4 feet, the radius ( r ) is half of the diameter:

[ r = \frac{4}{2} = 2 \text{ feet} ]

The height ( h ) of the cylinder is 5 feet. Now, substituting the values into the volume formula:

[ V = \pi (2)^2 (5) ]

[ V = \pi (4)(5) ]

[ V = 20\pi \text{ cubic feet} ]

Next, we can use the approximate value of ( \pi ) (about 3.14) to compute the volume numerically:

[ V \approx 20 \times 3.14 = 62.8 \text{ cubic feet} ]

Now that we have the volume, we can compute the