2. A container is in the shape of a truncated cone (frustum), which has volume 7rh V: ?(R2 +r2 +Rr), where R indicates the radius of the top of the truncated cone, 7" the radius of the bottom of the truncated cone, and It the height of the cone. As water is being poured into the container7 Use RC7 Tc, he, and VC to represent the dimensions of the container, and use R7 73 h7 and V to represent the dimensions of the water. NOTE: For this particular container, RC : 2 meters, 'I'C : 1 meter and he : 5 meters. Liquid is poured into this container so that the container is lling at a rate of 4 m3/s. (a) Draw a diagram of the truncated cone container using the labels of ROTC and hc. (1 point) (b) If the height of the container he 2 5, then draw and label a \"snapshot\" of the liquid in the truncated cone when the liquid is at a height of h : 3 meters. What shape is the liquid? (1 point) NOTE: For this particular container, Rc = 2 meters, rc = 1 meter and he = 5 meters. Liquid is poured into this container so that the container is filling at a rate of 4 m3/s. (c) Find an equation relating h to R. (If h = 5, what is R? When h = 0, assume that R = rc.) Use the remaining space on this page to list down things you know about variables that are relevant to this problem. (2 points)(d) When the liquid is at a height of 3 meters, how fast is the height of the liquid in the container changing? (4 points) Hint: When constructing your equations7 ask yourself: Is 7", the radius of the bottom of the liquid, changing? What is h a function of? (e) When the liquid is at a height of 3 meters, how fast is the radius of the surface of the liquid, R, growing? (2 points)