No, I believe it is not possible unless you make additional assumptions about the sides of the prism.
I suppose that you have a triangular prism, i.e. each end is a 30-60 right triangle and the 3 sides are rectangles. The volume of that solid is (1/2)s2√3*L where s is the smaller side of the triangular end and L is the length of the prism.
Paul M.
tutor
Yes. Use the “formula” I gave you. If L=30 & you know the Volume, then you can calculate s, the shorter side.
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09/17/19
Alyssa H.
Awesome! So my numbers do not appear to be adding up when I solve for s. I'm getting 26.9 cm and when I plug this back in, my volume is only 18799.9. Could you assist with the order of operations? Additionally, if I calculated the base and height of the side triangles successfully using the above formula, could I change two of the angles on the triangle (not the right angle) and figure out what the new dimensions would be while still having the total volume equal to 18927cm cubed (about 5 gallons)? For example if I change the triangle angles to be 90, 40, 50. or 90, 70, 20, is it possible to calculate what the dimensions would be if i know the volume and length of the prism? Or would this require a completely different formula than the one above?
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09/18/19
Paul M.
tutor
The answer I got is actually 26.990821 and I suspect you may need to carry all the digits to get the volume correct...you probably have round-off error. The volume of the prism is the area of the triangular base times the altitude. If you change the shape of the triangle, the area will change. In the new situation the easiest way to calculate the area is (1/2) the product of any two sides times the sin of the angle between them.
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09/18/19
Alyssa H.
yes using the exact values worked! I am still pretty stumped on how to acquire the dimensions of the triangle bases if I only know the volume (18927.1 cm cubed) and the altitude (30cm) and the triangle angles (90, 40, 50 or 90, 70, 20). Do you mean the product of any two sides of the triangles? So if the triangles are not nice 30, 60 90 angles. Would I need to know at least one of the sides lengths in order to figure out the rest?
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09/18/19
Paul M.
tutor
The volume of the prism is the product of the area of the triangular base times length of the prism, i.e. the area of the triangular base is the quotient of the volume divided by the length. There is always a relation between the 2 legs of a right triangle: if s is a leg and A is the angle adjacent to the leg, then the other leg is s tan A and the area of the triangle is (1/2)( s^2) tan A. If it is not a right triangle, then you need to have more information about the triangle to determine the relation among the sides...this is what the study of trigonometry is all about. I hope this helps.
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09/18/19
Alyssa H.
Thank you for your responses!
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09/23/19
Alyssa H.
Thank you. What if I assumed the depth or length of the prism was 30cm, would I be able to calculate the rest of the sides then?09/17/19