11. Angela is using several cones to decorate for a party. The cones she has chosen are 8 inches tall and have a radius of 3 inches. What is the volume of
one of the cones to the nearest whole cubic inch?

Step-by-step explanation:

First start with your cone volume equation which is

Now plug in what you know

r=3

h=8

put in calculator and get

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.