You are designing a container in the shape of a cylinder. The radius is 5 inches. You want the container to hold at least 725π cubic inches. What is the least possible height of the container?

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Answer 1 · 2018-06-07T21:42:18

#color(blue)("height">=145 " in")#

The volume of a right cylinder ( sides perpendicular to base ) is given by:

#"Volume"="area of base"xx"height"#

We are given #"radius"=5# so the area of the base is fixed. This is given by:

#"Area"=pir^2#

So:

#A=pi(5)=5pi#

To hold at least #725pi# cubic inches.

So we have:

#5pi*h=725pi#

#h=(725pi)/(5pi)=145" inches"#

The hight has to be a minimum of #145 " inches"#. We write this as:

#"height">=145 " in"#