Use cylindrical coordinates. Find the volume of the solid that is enclosed by the cone
z = \sqrt{x^2+y^2} and the sphere x2 + y2 + z2 = 32.

You're locked out of your house. the only open window is on the second floor, 25 feet above the ground. there are bushes along the edge of the house, so you will need to place the ladder 10 feet from the house. what length ladder do you need to reach the window?