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Question 1003131: I need to get a calculation and a drawing to an octagonal prism that will hold 500 ml of liquid please for an assignment
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the formula for the volume of an octagonal prism is:
v = 2 * (1 + sqrt(2)) * a^2 * h
a is one side of the octagonal base.
h is the height.
if v = 500, then the formula becomes:
500 milliliters = 2 * (1 + sqrt(2)) * a^2 * h
liters are measures of volume of liquid.
the prism is probably measured in centimeters or millimeters.
you would need to convert from milliliters to cubic millimeters or something to allow you to construct your octagonal prism.
1 milliliter is equal to 1000 cubic millimeters.
that's the conversion factor.
500 milliliters is therefore equivalent to 500,000 cubic millimeters.
your equation becomes:
500,000 cubic millimeters = 2 * (1 + sqrt(2)) * a^2 * h
all that's left is to assume the value of one of the variables and then solve for the other.
assuming your container is going to be 1000 millimeters high, then the equation becomes:
500,000 cubic millimeters = 2 * (1 + sqrt(2)) * a^2 * 1000
now you can solve for a to get a = 10.17611864 millimeters.
your equation then becomes:
500,000 cubic millimeters = 2 * (1 + sqrt(2)) * 10.17611864^2 * 1000 which becomes:
500,000 cubic millimeters = 500,000 cubic millimeters.
this confirms the solution is correct.
500,000 cubic millimeters is equivalent to 500 milliliters.
now you can play with the numbers to get what you want.
for example, assume the height is only 500 millimeters high and then solve for a^2,
a is one side of the octagonal base.
h is the height of the octagonal prism.
the formula i am using was obtained from the following link.
https://www.google.com/?gws_rd=ssl#q=volume+of+an+octagonal+prism
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