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three sides of cube


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Kirill Z. | Physics, math tutor with great knowledge and teaching skillsPhysics, math tutor with great knowledge...
4.9 4.9 (174 lesson ratings) (174)
If it is a cube, then its volume V=a3, where a is the side of a cube.
Thus, a=³√V; 
In your case; a=³√500≈8 cm
For the second case,
a=³√800≈9 cm
George T. | George T.--"It's All About Math!"George T.--"It's All About Math!"
I'm not sure what the question is.  I assume it is to determine the length of each side of the cube with the volume shown.
So for a given Volume of 500 cm3, each side would have a length of the cube root of 500 cm3 or 5001/3 cm3.
This can be simplified, through factoring:  5001/3 = (2*2*5*5*5)1/3 = (5*41/3) cm is the length of each side (read as 5 times the cube root of 4)
Similarly, for 800 cm3, each side would have a length of
8001/3 = (2*2*2*2*2*5*5)1/3 = 2*1001/3 cm (read as 2 times the cube root of 100).
Hope this helps!
George T.
Elias H. | Patient and Knowledgeable Liberal Arts Math TutorPatient and Knowledgeable Liberal Arts M...
4.7 4.7 (25 lesson ratings) (25)
In this question you have been given the volume and seek the side lengths. It is as simple as a cube root! The answers here may be written concisely as 500cm3^(1/3) and 800cm3^(1/3). That is about 7.9cm and 9.3cm as the actual side lengths.