Sides of Two Cubes
The difference between the sides of two cubes is 6, and the difference in their volumes is 504.
Find the sides of the cubes!
Find the sides of the cubes!
posted by Zaux at
9:05 PM
Friday, January 1, 2010
Links
Search
Share
- Tom Chrome Extension
- ToM @ Twitter
- MeeT ToM
- Daily Tricks Widget
- Vista Gadget 1.5
- iPhone Widget
- Windows XP Widget
- Google Toolbar Button
- Suggestions
Favorite Links
- Vista Sidebar Gadgets
- Widgets for Web 2.0
- C Sharp Tricks
- Interview Information
- Illustrator - Elar Alexander
Bookmark Us
Previous Posts
- Happy New Year
- Stealing Wine
- Gold Bars in a Pile
- A Particular Square Number
- Rabbits and More Rabbits
- Fashion Show
- The Mutilated Chessboard
- Strange Signs
- Mad Nomads
- Alien Ages
3 Comments:
R1-R2=6
V1-V2=R1^3-R2^3=504
V1-V2=(R2+6)^3-R2^3
V1-V2=(R2+6)^2*(R2+6)-R2^3
V1-V2=(R2^2+12*R2+36)(R2+6)-R2^3
V1-V2=(R2^3+12*R2^2+36*R2+6*R2^2+72*R2+216)-R2^3
V1-V2=18*R2^2+108*R2+216=504
18*R^2+108*R2-288=0
quadratic formula applies to find 0s
R=(-b+/-sqrt(b^2-4*ac))/(2*a)
R=(-108+/-sqrt(108^2+4*18*288))/(2*18)
R=2,-8
Discard -8, as side must have positive length
Side length of R2=2
R1 has side length of 8
Check answers
R2-R1=8-2=6
R1^3-R2^3= 512-8=504
Answer:
The larger cube has side length of 8, and volume of 512
The smaller cube has side length of 2, and volume of 8
Cam
Nicely done ...
Thank's Zaux. Nice problem. Thank you for posting it.
Cam
Post a Comment
Links to this post:
Create a Link
<< Home