Calculus and vectors Question plz help ASAP, ANSWER FULLY PLZ

Hypothesis: The rate of change of the volume of a sphere is proportional to its surface area. Experiment: a) Obtain a spherical lollipop on a stick. Assume that it is a perfect sphere. Measure and record the initial radius of this sphere. (Hint: Remember the relationship between radius and circumference). b) Place the lollipop in your mouth and carefully consume it (uniformly) for 30 s. Measure and record the new radius in a table similar to the one here. Repeat until you have at least ten measurements. Time (s) 30 60 90 120 150 180 210 240 270 300 Radius of Lollipop (cm) c) Use your data to determine the rate of change of radius with respect to time. Write an equation to model the radius as a function of time, Justify your choice of models. d) Write the formula to model the volume as a function of the radius. Use your equation from part c) to model the volume as a function of time. e) Use your model from part c) to calculate the rate of change of volume with respect to time when the radius has reached half its original value. f) Explain why you should not expect the rate of change of volume with respect to time to be constant in this situation. g) Use your model to estimate how much time is required to completely consume the lollipop. h) Does this experiment confirm the hypothesis? Explain. i) How would the time to consume the lollipop change if the initial radius were multiplied by a constant k? Justify your response