SOLUTION: 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 cen

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. What are the roots of the equation? What is the domain that makes sense for this problem? Explain your reasoning. Calculate the volume for each integer value x in this domain. For what integer value of x is the volume of the cone a maximum?
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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 = is volume of a cone
let x = no. of cm increases and no. of 4cm decreases
V(x) =

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
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