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. ∫10 0 π (2 - y/5)^2 dy
1. Which is the shape of the region being integrated?
O Cone
O Hemisphere
2. radius/radius and height = (Enter the radius, or the radius and height separated by a comma, e. g., 4. 3)
3. volume =
B. ∫14 0 π(196 - h^2) dh
1. Which is the shape of the region being integrated?
O Cone
O Hemisphere
2. radius/radius and height = (Enter the radius, or the radius and height separated by a comma, e. g., 4, 3)
3. volume =