Ch $6$ Classwork, Calculator Active

Suppose a sump pump, used to pump excess liquid from a location, has a bucket that is the shape of a frustum of a cone as shown. The base of the pump bucket is the smaller circle with a diameter of $1$ ft and the top of the bucket is the larger circle with a diameter of $3$ ft $.$ The bucket is $3$ ft tall.

Use the sump pump bucket described above to answer the following questions:

If the liquid in the bucket is a mixture of water and sewage with a density of $45l\frac{b}{f}{t}^3,$ calculate the total mass of the liquid.

If the pump is set up to pump liquid vertically out of the bucket to a drain that is located at ground level which is $10$ ft above the top of the bucket, how much work is required to empty a completely full bucket?