Quiz: Related Rates
Problem 1: Imagine an inverted right circular cone of height 5m and radius 3m filled to the brim with sand. It is located above a right cylinder of height 10m and width 15m. Find the rate at of which the pile of sand is growing in the cylinder if the depth of the sand in the cone is decreasing at a rate of 0.5m/s and is at a depth of 3m. Assume that the sand that flows into the cylinder uniformly.
Problem 2: A man 2 meters tall is walking at a constant rate of 1 m/s away from a 5 meters tall light post. At what speed is the tip of his shadow moving when he is 10 meters away from the light post?
Problem 3: A man 1.5 meters tall is jogging at a constant rate of 2 m/s towards a 3.5 meters tall light post. At what speed is the tip of his shadow approaching the lightpost, regardless of where he is?