3. A collection of geometrical problems on related rates. a) The volume of a cube is decreasing at the rate of 10 m3/hr. How fast is the total surface area decreasing when the surface area is 54 m2? b) Rachael is blowing up a balloon so that the diameter increases at the rate of 10 cm/ sec. At what rate must she blow air into the balloon when the diameter measures 4 cm? c) The area of an equilateral triangle is increasing at the rate of 5 m2 / hr. Find the rate at which the height is changing when the area is 64\\// 3 m2. 4. The trough shown below is 5 feet long and its vertical cross sections are inverted isosceles triangles with base 2 feet and height 3 feet. Water is being siphoned out of the trough at the rate of 2 cubic feet per minute. At any time t, let h be the depth and V be the volume of water in the trough. a) Find V when the trough is full. 1 b) What is the rate of change in h at time t = t1 when the trough is 1 full by volume? c) What is the rate of change in the area of the surface of the water at t = t1