(1 point) All edges of a cube are expanding at a rate of 9 centimeters per second. We will find out how fast the surface area is changing when each edge is 6 centimeters long and when each edge is 22 centimeters long. Find an equation relating the edge-length I to the surface area S. Remember that a cube has 6 faces. S= square centimeters (use a capital "L" for edge-length.) Differentiate this equation with respect to time to obtain a formula for dS/dt in terms of L and d L/dt: dSldt = square centimeters per second Now use what you know about d L/dt to compute dS/dt when L = 6: When L = 6, dSldt = square centimeters per second Now use what you know about d L/dt to compute dS/dt when L = 22: When L = 22, dSldt = square centimeters per second(1 point) A 20-foot ladder is leaning against a house. The top of the ladder slips down the wall at a rate of 1.5 feet per second. When the base of the ladder is 16 feet from the wall, how fast is the base of the ladder moving away from the wall? The base is moving at feet per second. When the base of the ladder is 12 feet from the wall, how fast is the base of the ladder moving away from the wall? The base is moving at feet per second. (1 point) A spherical balloon is inflated with air at a rate of 90 cubic feet per minute. Find the rate of change of the radius of the balloon when the radius is 7 feet. The radius is changing at feet per minute. Find the rate of change of the radius of the balloon when the radius is 8 feet. The radius is changing at feet per minute. (1 point) A dump truck dumps gravel, forming a conical pile. The volume of the pile increases at a rate of 7 cubic feet per second. The height of the cone is related to the radius by h = 2r. The volume of the cone is given by V = 1/3ihr2. Find the rate of change of the radius of the cone when the radius is 14 feet. The radius is changing at feet per second. Find the rate of change of the radius of the cone when the radius is 30 feet. The radius is changing at feet per second.(1 point) An air traffic controller spots two airplanes at the same altitude converging to point A as they fly at right angles to each other. One airplane is 200 miles from point A and has a speed of 800 miles per hour. The other is 230 miles from point A and has a speed of 920 miles per hour. At what rate is the distance between the two planes changing? Think carefully about whether this rate should be positive or negative. The distance is changing at miles per hour.(1 point) An accident at an oil drilling platform is causing a circular oil slick. The slick is 0.11 feet thick, and when its radius is 400 feet, the radius is increasing at a rate of 0.4 feet per minute. At what rate is oil flowing from the site of the accident? The oil is flowing at cubic feet per minute.(1 point) The radius r of a sphere is increasing at a rate of 7 inches per minute. We will find the rate of change of the volume of the sphere when r = 10 inches and when r = 24 inches. An equation involving V and r is V = 4/3ar3. Differentiate this equation with respect to time to obtain a formula for dV /dt in terms of r and dr/dt : dV ldt = cubic inches per minute Now use what you know about dr/dt to compute dV/dt when r = 10: When r = 10, dV /dt = cubic inches per minute Now use what you know about dr/dt to compute dV/dt when r = 24: When r = 24, dV /dt = cubic inches per minute