Question
QUESTION: Two square boxes have the following volumes:

Larger box - 13,856 square inches.

Smaller box - 6,928 square inches.

The larger box is twice the height of the smaller box.

Calculate dimensions of each box.  Thank you.

ANSWER: Hi, I can't answer the question the way it is stated. Perhaps you can review it, fix it, and send it again?
The problem is a 'square box' is a cube and thus all three dimensions need to be the same so one can't
have twice the height of the other because then it wouldn't be a cube. The writer of the problem might of
said 'square bases', that would work. The other problem with the question is the units. The writer talks
about 'square' inches and volume, and volume is cubic units, area has square units.i am pretty sure since
the writer is talking 'boxes' and one height being twice the other height that the problem is about volume.
So please review and amend the problem so I can answer it for you.

Prof W

---------- FOLLOW-UP ----------

QUESTION: Dimensions Follow-up:

Larger box-  should be 13.856 cubic inches.

smaller box- should be 6.928 cubic inches.

The larger box IS twice the height of the smaller according to the problem.

Calculate dimensions of each box.  Thanks.

Hi Randy~
I still need to know if the following problem statement is correct: two square boxes have the following volume.
If so, then one height canNOT be twice the other height because one volume is twice the volume of the other and and you would get the double volume from doubling one of the dimensions. AND a square box is a cube (length, width, height all the same) and if one is a cube the other canNOT be a cube too with the height doubled and the volume doubled. This is why I asked if the problem statement was square base and even then you can't give numerical dimensions because there is not enough information given in the problem. The best one could do is answer for one variable in terms of the other variable.
In this problem if the base is a square then call those sides s and the height of the smaller box is s also since a square BOX is a cube because a cube has all dimensions the same and the height of the larger box is 2s, and then we have
smaller box volume: 6.928 = s^3 and larger box volume: 13.856 = 2s*s^2 = 2s^3. The larger box reduces to the same as the smaller box. If the smaller box is indeed square then all dimensions are the same and we have 6.928 = s^3, taking the cube root of both sides we have
APPROXIMATELY s = 1.9063499 or about 1.90635 since (1.90635)^3 = 6.928000594297875, pretty darn close to 6.928. So s approximately equal to 1.90635 in.
If the question is not worded correctly please send it again.
Thanks,
Prof W

Volunteer

##### Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

##### Experience

I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

Education/Credentials
I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

Awards and Honors
Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0