So the volume of the cylinder = pi r^2 * h
Height = 4 feet tall
Radius = 1 foot
So just do pi * 1^2 * 4
3.14 x 1^2 x 4 = 12.56 cubic feet
For the transformation

the Jacobian is

with determinant

The vertices of the triangle in the
-plane are



Then the integral is

Try the first four cards in order from left to right. It starts with the expression, plugs in 6 for t, does 6 * 3 first because of PEMDAS, and then does 27 - 18, which is 9.