Question 1101549
a woodworker makes different sizes of wooden blocks in the shape of cones.
 the narrowest block the worker makes a radius r=8 centimeters and a height h=22 centimeters.
 For each centimeter increase in the radius the worker decreases the height of the cone four centimeters.
 Write a function V(x) to represent the volume of each cone the worker makes as a function of x.
V = {{{1/3}}}{{{pi*r^2*h)}}} is volume of a cone
let x = no. of cm increases and no. of 4cm decreases
V(x) = {{{1/3}}}{{{pi*(8+x)^2 * (22-4x)}}}
 What are the roots of the equation?
x = -8
and
-4x = -22
x = +5.5
 What is the domain that makes sense for this problem?
x=0 to x=5
When x > 5 the height becomes a neg number
:
 Calculate the volume for each integer value x in this domain.
 x | V(x)
----------
 0 | 1474.5
 1 | 1526.8 Max volume
 2 | 1466.1
 3 | 1267.1
 4 | 904.8
 5 | 353.9
:
 For what integer value of x is the volume of the cone a maximum? x = 1