I have a problem in my book that i cant seem to figure out how they got the radius or weight.
Problem: An open tank has the shape of a right circular cone(see figure). The tank is 8 feet across the top and 6 feet high.
How much work is done in emptying the tank by pumping the water over the top?
I will attach the figure from the book.
I took half of the right side of the shape and drew a rectangle so it could be revolved around the y axis to make its shape.
Volume of disk \(\displaystyle \pi r^2\)
the solutions manual gives \(\displaystyle \pi( \frac{2}{3}y )^2 dy \)
How are they getting 2/3 y?
they are also getting a weight of disk 62.4 not sure where that came from since its not specified.
Problem: An open tank has the shape of a right circular cone(see figure). The tank is 8 feet across the top and 6 feet high.
How much work is done in emptying the tank by pumping the water over the top?
I will attach the figure from the book.
I took half of the right side of the shape and drew a rectangle so it could be revolved around the y axis to make its shape.
Volume of disk \(\displaystyle \pi r^2\)
the solutions manual gives \(\displaystyle \pi( \frac{2}{3}y )^2 dy \)
How are they getting 2/3 y?
they are also getting a weight of disk 62.4 not sure where that came from since its not specified.