Each of the following integrals represents the volume of either a hemisphere or a cone, and the variable of integration measures a length. In each case, say which shape is represented and give the radius of the hemisphere or radius and height of the cone. Make a sketch of the region, showing the slice used to find the integral, labeling the variable and differential on your sketch. Then evaluate the integral to find the area.

A. $\int_0^{6} \pi(3 - y/2)^2\,dy$
Which is the shape of the region being integrated?
A. Cone
B. Hemisphere

radius/radius and height =
(Enter the radius, or the radius and height separated by a comma, e.g., 4, 3)

volume =

B. $\int_0^{7} \pi(49 - h^2)\,dh$
Which is the shape of the region being integrated?
A. Cone
B. Hemisphere

radius/radius and height =
(Enter the radius, or the radius and height separated by a comma, e.g., 4, 3)

volume =