Use the scoring guide below to determine the score the student would earn and explain your answer. A container has the shape of an open right circular cone, as shown in the figure above. The height of the container is 10 cm and the diameter of the opening is 10 cm. Water in the container is evaporating so that its depth is is changing at the constant rate of 1: cm/hr. (The volume of a cone of height h and radius r is given by V = (a) Find the volume V of water in the container when it = 5 cm. Indicate units of measure. |-lOcm--{ 1 2 wk.) (b) Find the rate of change of the volume of water in the container, with respect to time, when h = 5 cm. Indicate units of measure. (c) Show that the rate of change of the volume of water in the container due to evaporation is directly proportional to the exposed surface area of the water. What is the constant of proportionality? 5 1 52 125 (a) When5, r-s. Van545) 5_ Ear cm 1* 5 1 (b)i_10's'=h -1 _2 _i a._l 2d_h V'alaih iii123\"\" (1:5 '4\"hdt dV _1 cm dtL=5_4\"(25)(1 iol=135 \" X: 0B dV_ 2 air ;d_r=l E'slrdhl- dt +cT2rh 'dt 2d: dV 1 25 3 5 3 T: -5,-;'\"llill'nl+2(2l5l all 15 3 dV 1 2dh__3 2 (0) dc 4hdt_ 40" __i 2__ 2___ 4071121\") 101w 10 area. 3 The constant of proportionality is _E' units of ma in (a) and aha/(r in (b) 3 1:thenh=5 1: r=hin(a)or(b) V as a. function of one variable in (a) or (b) 1 : OR 5 d; dt i all: chain rule or product rule error 1 : evaluation at h = 5 2: 1: shows =1r- area dt : identies constant of proportionality 1 : correct unite in (a) and (b)