Answer:
Step-by-step explanation:
The volume of a cylinder is given by the formula
[tex]Vcylinder=\pi r^2h[/tex]
and the volume of a cone is given by the formula
[tex]Vcone = \frac{1}{3} \pi r^2h[/tex]
where r is the radius of the base of the cylinder (which is the same as the base of the cone since they make up one tank), and
h_{cylinder}
and
h_{cone}
are the heights of the cylinder and cone respectively.
Given that the height of the cylinder section is 2ft and the height of the cone section is 1ft, the total volume of the tank (in cubic feet) is
[tex]Vtotal=Vcylinder+Vcone=\pi r^2(2+\frac{1}{3} )[/tex]
The client wants the tank to hold between 200 and 250 gallons of water. Since 1 gallon is approximately 0.133681 cubic feet, this corresponds to a volume of between 26.7362 cubic feet and 33.42025 cubic feet.
Setting these volumes equal to the total volume of the tank gives us the following equations:
For the lower limit:
[tex]26.7362 =[/tex] [tex]\pi r^2 (2 + \frac{1}{3})$[/tex]
And for the upper limit:
[tex]$33.42025 = \pi r^2 (2 + \frac{1}{3})$[/tex]
Solving these equations will give us the range of possible values for r, the radius of the tank. Note that the actual value chosen for r would depend on other factors such as the available space and the cost of materials.
