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| PAGE: 146 | SET: Exercises | PROBLEM: 50 |
(a).
The company sells cylindrical oil container with a capacity of 
liters.
liter 
c.c
Therefore the volume of the container 
is 
c.c.
The formula for the volume of the container is 
.
Now subustiute volume 
in the formula 
.
The formula for the surface area of the cylinder is 
.
Now subustiute 
in the formula 
.
.
The surface area of the cylinder in terms or radius is given by 
.
(b).
The company wants the surface area of the cylinder to be less than 
sq.cms
Subustiute 
in the equation 
.
The inequality can be written as 
.
(c).
The inequality is 
.
Let 
.
Draw the coordinate plane.
Graph the function 
.
Graph :
.gif)
Observe the graph :
The zeros of the graph are at 
and 
.
The graph is undefined at 
.
The solutions of are 
values such that 
is negative.
From the graph the solution set is 
.
Since the radius is not in negative terms, only possible values are to be considered.
Therefore the radius of the cylinder is between 
cms to 
cms.
(a).
The surface area of the function as a radius is given by .
(b).
The inequality can be written as .
(c).
Graph :
Therefore the radius of the cylinder is between 
cms to 
cms.
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