How much does a solid aluminum cylinder weighing 165 pounds per cubic foot measure with a diameter of 4 feet and a height of 5 feet?

To determine the weight of the solid aluminum cylinder, we need to find its volume first. The formula for the volume of a cylinder is:

[ V = \pi r^2 h ]

where ( r ) is the radius and ( h ) is the height of the cylinder.

Given that the diameter of the cylinder is 4 feet, the radius ( r ) is half of that, which is 2 feet. The height ( h ) is given as 5 feet. Plugging these values into the volume formula:

[ V = \pi (2 \text{ ft})^2 (5 \text{ ft}) ] [ V = \pi (4 \text{ ft}^2) (5 \text{ ft}) ] [ V = 20\pi \text{ ft}^3 ]

Now, to calculate the actual volume using the approximate value of ( \pi ) (3.14):

[ V \approx 20 \times 3.14 = 62.8 \text{ ft}^3 ]

Next, we need to find the weight of the cylinder. The weight can be calculated by multiplying the volume by the density of aluminum, which