Math 251 Written Homework 8 - W23 Due Thurs. March 2, 2023 (2) (Related Rates) A spherical scoop of ice cream is melting (losing volume) at a rate of 3cm3 per minute. (a) Write a mathematical statement that represents the rate of change of the volume of the sphere as described in the problem statement. (Include units in your statement.) (b) The radius of the scoop, r(t), in centimeters, is also decreasing with respect to time, t, (minutes). Is # positive, negative, or zero? Explain. (c) What are the units of the derivative dr? (d) The volume of a sphere, V, written as a function of the radius, r, is V(r) = 4mr3. Use implicit differentiation and the chain rule to find . Page 3 of 5Math 251 Written Homework 8 - W23 Due Thurs. March 2, 2023 (e) We will want to find the rate of change of the radius for a variety of lengths of the radius. To aid in this process, solve your equation from part (d) for ". (f) At what rate is the radius changing when the radius is 5cm? 4cm? 3cm? (g) As time goes on, make an educated guess what happens to the rate of change of the radius, d . Page 4 of 5Math 251 Written Homework 8 - W23 Due Thurs. March 2, 2023 (h) As time t goes to infinity: (i) What happens to the rate of change of volume, ? You are solving for this limit: lim dV 1-+oo dt (ii) What happens to the volume, V(t)? Write down the limit you are solving for. (iii) What happens to the radius, r(t)? Write down the limit you are solving for. (iv) What happens to the rate of change of the radius, If? Write down the limit you are solving for. Page 5 of 5