Find Unknown Variables a, b, c in V=abc Equation | Volume 512cm^3

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Homework Help Overview

The problem involves finding the unknown variables a, b, and c in the equation V = abc, given that the volume is 512 cm³ and the relationships a = 2b and b = 2c. Participants are exploring how to express these variables in terms of one another.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss rewriting the volume equation in terms of a single variable, specifically focusing on the relationships between b and c. There is an exploration of the implications of substituting these relationships into the volume equation.

Discussion Status

Some participants have provided guidance on expressing the volume in terms of c, leading to the formulation of V = 8c³. There is a progression in the discussion as participants verify calculations and relationships, although no explicit consensus is reached on the final values of a, b, and c.

Contextual Notes

The original poster's constraints include the specific volume of 512 cm³ and the relationships between the variables, which are central to the discussion but not fully resolved.

besfort
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Homework Statement


The volume is 512cm^3. Known as V=abc; a = 2b, b = 2c. Find a, b, c


Homework Equations


V = 512cm^3.
a = 2b
b = 2c


The Attempt at a Solution


V=2b * 2c * c
V=2b * 2c^2
512cm^3=2b * 2c^2
 
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besfort said:
512cm^3=2b * 2c^2

You know the relation between b and c, so you can write this expression in terms of 1 variable.
 
So this would be written as 2 * 2c * 2c^2 which would result to 8c^3, right?
 
besfort said:
So this would be written as 2 * 2c * 2c^2 which would result to 8c^3, right?

Yes :-)
 
I came to the result where V=8c^3 and c = 4 cm. Then b was found from the equation of 2c, and a was found by the equation of 2b.

I came to the result;
a = 16cm,
b = 8cm,
c = 4cm

V = 16cm * 8cm * 4cm
V = 512 cm^3

Which is correct. Thank you for the help!
 

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