If the mountain is increasing in height at 2 feet per hour

Question

The 12 inch base of a right triangle is growing at 3 inches per hour, and the 16 inch height is shrinking at 3 inches per hour.

a. Is the area increasing or decreasing?

b. Is the perimeter increasing or decreasing?

c. Is the hypotenuse increasing or decreasing?

2. Lava flowing from a hole at the top of a hill is forming a conical mountain whose height is always the same as the width of its base (Figure). If the mountain is increasing in height at 2 feet per hour when it is 500 feet high, how fast is the lava flowing (how fast is the volume of the mountain increasing)? ( V = 1/3 πr²h)

3. The string of a kite is perfectly taut and always makes an angle of 35^o above horizontal.

a. If the kite flyer has let out 500 feet of string, how high is the kite?

b. If the string is let out at a rate of 10 feet per second, how fast is the kite's height increasing?