You are blowing air into a spherical balloon at a rate of 11 cubic inches per second. Given that the radius of the balloon is 3 inches when t = 3 seconds answer the following questions: (a) How fast is the radius of the balloon growing at t = 3 seconds Answer. E inches per second. (b) What is the rate of change of the surface area at t = 3 seconds? Answer E square inches per second.The height of a triangle is increasing at a rate of 2 cm/min while the area of the triangle is increasing at a rate of 8 square cm/min. At what rate is the base of the triangle changing when the height is 1 centimeters and the area is 3 square centimeters? Answer: E cm/min.A filter filled with liquid is in the shape of a vertex-down cone with a height of 9 inches and a diameter of 6 inches at its open (upper) end. If the liquid drips out the bottom of the filter at the constant rate of 1 cubic inches per second, how fast is the level of the liquid dropping when the liquid is 2 inches deep? Answer: E in/sec. Hint: Recall the similar triangle property.A trough is / = 10 ft long and has a cross section of an isosceles trapezoid with base of b = 3 ft, height of h = 1 ft, and top of t = 6 ft (see picture below). b (You can click on the graph to enlarge the image.) If the trough is being filled with water at a rate of 10 fto min how fast is the water level rising when the water is 2 inches deep? Answer. E ft/min