SOLUTION: Find the dimensions of a cylindrical container with a volume of 40 cubic inches and a side area of 60 square inches

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Question 1036916: Find the dimensions of a cylindrical container with a volume of 40 cubic inches and a side area of 60 square inches
Found 3 solutions by josgarithmetic, ankor@dixie-net.com, MathTherapy:
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Putting into variables,
system%28v=40%2Ca=60%29

Apply some formulas, implying variables' meanings,
system%28a=2%2Ar%2Api%2Ah%2Cv=pi%2Ar%5E2%2Ah%29
The unknown variables being r for radius, and h for "length" or height of the cylinder. Top and bottom are ignored, or assumed as open.


ALGEBRA STEPS
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r=a%2F%282pi%2Ah%29
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pi%2Ar%5E2%2Ah=v
r%5E2%2Ah=v%2Fpi
%28a%2F%282pi%2Ah%29%29%5E2%2Ah=v%2Fpi
%28a%5E2%29%2F%284pi%5E2%2Ah%5E2%29h=v%2Fpi
%28a%5E2%29%2F%284pi%2Ah%29=v%2Fpi
a%5E2%2F%284pi%29=vh%2Fpi
h=%28pi%2Fv%29%28a%5E2%2F%284pi%29%29
highlight%28h=a%5E2%2F%284v%29%29
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The value for h should be 60%5E2%2F%284%2A40%29=3600%2F160=360%2F16=180%2F8=90%2F4=highlight%2845%2F2=22%261%2F2=h%29

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Find the dimensions of a cylindrical container with a volume of 40 cubic inches and a side area of 60 square inches
:
let r = the radius of the container
let h = the height
:
Volume: pi%2Ar%5E2%2Ah = 40 cu/in
h = 40%2F%28pi%2Ar%5E2%29
:
Side area: 2%2Api%2Ar%2Ah = 60 cu/in
divide both sides by 2
pi%2Ar%2Ah = 30
h = 30%2F%28pi%2Ar%29
:
h=h, therefore
40%2F%28pi%2Ar%5E2%29 = 30%2F%28pi%2Ar%29
multiply both sides by pi*r
40%2Fr = 30
30r = 40
r = 40/30
r = 11%2F3 inches is radius
Find h
h = 30%2F%28pi%2A1.333%29
h = 7.164 inches is the height
:
:
Confirm these values in the Vol formula
V = pi%2A1.333%5E2%2A7.164
V = 40

Answer by MathTherapy(10549) About Me  (Show Source):
You can put this solution on YOUR website!

Find the dimensions of a cylindrical container with a volume of 40 cubic inches and a side area of 60 square inches 
Radius: highlight_green%28matrix%281%2C2%2C+1%261%2F3%2C+inches%29%29

Height: highlight_green%28matrix%281%2C4%2C+90%2F%284%2Api%29%2C+or%2C+7.161972%2C+inches%29%29