The areas of the faces of a rectangular box are 84 cm2, 70 cm2 and 30 cm2.
What is the volume of the box?
Use algebra to solve the problem.
Solution to the Problem:
The answer is 420 cm3Let x, y, and w represent the three length of the sides of the rectangular box.
Then you can write the following equations:
xy = 84
xw = 70
and yw = 30.
Then w = 70 / x and substitute it in equation 3 to obtain 70y / x = 30.
Solving for x, we get x = 70y / 30.
Substitute this in equation #1 to get 70y2 / 30 = 84
This yields y2 = 36, so y = 6 cm.
It follows that x = 14 cm and w = 5 cm.
Therefore, the volume is 6 x 14 x 5 = 420 cm3
Correctly solved by:
| 1. Christian Andersen |
Mountain View High School, Mountain View, Wyoming |
| 2. Jim Hooker | Johnson City, Tennessee |
| 3. Rosemary Walker |
Mountain View High School, Mountain View, Wyoming |
| 4. James Alarie | Flint, Michigan |
| 5. Martin Round | Studley, Warwicksire, United Kingdom |
| 6. Kimberly Howe | Tuscaloosa, Alabama |
| 7. Eliza Sheffield & Anna Vice | Tuscaloosa, Alabama |
| 8. Sierra Toomer |
Mountain View High School, Mountain View, Wyoming |
| 9. SreeRoopa Sankararaman | Singapore, Singapore | 10. Kylie Walker |
Mountain View High School, Mountain View, Wyoming |
| 11. Brijesh Dave | Mumbai city, Maharashtra, India |
| 12. Braydon D. Saxton |
Mountain View High School, Mountain View, Wyoming |
| 13. Hope Pfeifer |
Mountain View High School, Mountain View, Wyoming |
| 14. Britan Woody |
Mountain View High School, Mountain View, Wyoming |