In this assignment, you will consider two different situations involving cone-shaped objects that are in the process of getting smaller but in different ways. 1. First, consider a large pile of snow that has been pushed into approximately a cone shape by a snowplow. When we first look at the snow pile, we see that the pile is about 9 feet high, while the base of the cone has a diameter of approximately 10 feet. As the snow pile melts, the cone shrinks, but we assume that it keeps its overall proportions. a. Draw a diagram, showing the cone as it shrinks, and with variables labeling the important measurements. b. Write an equation for the volume of the cone, in terms of the variables you introduced in part (a). c. Write a constraint equation. (Hint: what isn't changing as the cone shrinks?) d. A basketball sits on top of the snowpile; as the cone shrinks. the basketball drops vertically. How fast is the basketball moving at a moment in time when the cone has a radius of 3 feet and the cone is losing 4 cubic feet of volume per hour? 2. Next, consider a pile of gravel at a construction site. Like the snow pile, the gravel pile is approximately cone-shaped, with an initial height of 9 feet and a base diameter of 18 feet. On a windy day, the gravel begins to slide down the sides of the pile; as it does so, the base of the pile gets wider, the height gets smaller, but the total amount of gravel in the pile does now change. a. Draw a diagram, showing the cone as it shrinks, and with variables labeling the important measurements. b. Write an equation for the volume of the cone, in terms of the variables you introduced in part (a). c. Write a constraint equation. (Hint: what isn't changing as the cone shrinks?) d. A basketball sits on top of the gravel pile; as the cone spreads out. the basketball drops vertically. How fast is the basketball moving at a moment in time when the cone has a height of 4 feet and the radius is growing at 2 cubic feet per minute