4 calculus questions

1. The area of a square is decreasing at the rate of 5cm^2/min. Find the rate of change of the length of a side when the side length is 15cm.


2. The base of a 13 m ladder is moved along a horizontal floor at the rate of 2m/sec away from the wall against which the ladder rests. At what rate is the top of the ladder moving down the wall when the top is 5 m above the floor.


3. Sand is poured on the ground forming a conical pile whose radius is twice its height. If the sand is poured onto the pile at the rate of 64 ft^3/min, how fast is the height changing when it is 8 feet?


4. The circumference of the circle is increasing at a constant rate of 6 inches per second. As the circle expands, the square expands to maintain the condition of tangency.

(A) Find the rate at which the perimeter of the square is increasing. Indicate units of measure.

(B) At the instant when the area of the circle is 25π square inches, find the rate of increase in the area enclosed between the circle and the square. Indicate units of measure.