5. ll edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the volume changing when each edge is 10 centimeters?

6. t a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 10 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. t what rate is the height of the pile changing when the pile is 15 feet high?

7. ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second.

(1) How fast is the top of the ladder moving the wall when its base is 7 feet from the wall? (2) Consider the triangle formed by the side of the house, the ladder, and the ground. Find the rate at which the area of the triangle is changing when the base of ladder is 7 feet from the wall.

(3) Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 7 feet from the wall.

8. Oil is falling from a conical funnel into a cylindrical container. The conical funnel has depth of 18 centimeters and diameter of 12 centimeters. The cylindrical container has diameter of 10 centimeters. The funnel was filled with solution in the beginning. When the height of oil in the funnel is 12 centimeters, the height is decreasing at a rate of 1 centimeter per minute. t what rate is the height of oil changing in the cylindrical container?