2008 iTest Problems/Problem 20
Problem
In order to earn a little spending money for the family vacation, Joshua and Wendy offer to clean up the storage shed. After clearing away some trash, Joshua and Wendy set aside give boxes that belong to the two of them that they decide to take up to their bedrooms. Each is in the shape of a cube. The four smaller boxes are all of equal size, and when stacked up, reach the exact height of the large box. If the volume of one of the smaller boxes is 
cubic inches, find the sum of the volumes of all five boxes (in cubic inches).
Solution
![[asy] import three; size(8cm); currentprojection=orthographic(1,1/2,1/2); draw((0,0,0)--(0,4,0)--(4,4,0)--(4,0,0)--(0,0,0)--(0,0,4)--(0,4,4)--(0,4,0)); draw((0,4,4)--(4,4,4)--(4,4,0)); draw((0,0,4)--(4,0,4)--(4,4,4)); draw((4,0,0)--(4,0,4)); for (int i=0; i<4; ++i) { draw((0,0,i)--(0,1,i)--(1,1,i)--(1,0,i)--(0,0,i)--(0,0,i+1)--(0,1,i+1)--(0,1,i),dotted); draw((0,1,i+1)--(1,1,i+1)--(1,1,i),dotted); draw((0,0,i+1)--(1,0,i+1)--(1,1,i+1),dotted); draw((1,0,i)--(1,0,i+1),dotted); } [/asy]](http://latex.artofproblemsolving.com/1/2/4/1240608b5c434c2679f3de2bdafa755220ba53d6.png)
The volume of one smaller cube is cubic inches, so each side length of a smaller cube is 
inches. That means the side length of the big box is 
inches, so the volume of the big box is 
cubic inches. Thus, the total volume of all five boxes is 
cubic inches.
See Also
| 2008 iTest (Problems) | ||
| Preceded by: Problem 19 |
Followed by: Problem 21 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 • 51 • 52 • 53 • 54 • 55 • 56 • 57 • 58 • 59 • 60 • 61 • 62 • 63 • 64 • 65 • 66 • 67 • 68 • 69 • 70 • 71 • 72 • 73 • 74 • 75 • 76 • 77 • 78 • 79 • 80 • 81 • 82 • 83 • 84 • 85 • 86 • 87 • 88 • 89 • 90 • 91 • 92 • 93 • 94 • 95 • 96 • 97 • 98 • 99 • 100 | ||
