SOLUTION: If a cubic yard of sand weighs 1.5 (US) tons, how many 11x6x7 inch ammo boxes can be completely filled with 1 ton of sand?

Algebra ->  Volume -> SOLUTION: If a cubic yard of sand weighs 1.5 (US) tons, how many 11x6x7 inch ammo boxes can be completely filled with 1 ton of sand?      Log On


   

Question 1159948: If a cubic yard of sand weighs 1.5 (US) tons, how many 11x6x7 inch ammo boxes can be completely filled with 1 ton of sand?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
a cubic yard of sand weighs 1.5 tons.
stated another way, 1.5 tons would fill a cubic yard.

1 ton of sand would therefore fill 1/1.5 * a cubic yard.
1/1.5 * 2/2 = 2/3.
1 ton of sand would therefore fill 2/3 * a cubic yard.

1 cubic yard has a volume of 46656 cubic inches.
2/3 of a cubic yard has a volume of 2/3 * 46656 = 31104 cubic inches.

an 11 by 6 by 7 inch ammo box has a volume of 462 cubic inches.

31104 cubic inches / 462 cubic inches = 67.32467532.

this says that a volume of 31104 cubic inches is equivalent to the total volume of 67.32467532 ammo boxes with a volume of 462 cubic inches each.

that's 67 ammo boxes completely filled with sand plus 1 ammo box that is filled to .32467532 of its capacity.

67 * 462 = 30954 cubic inches.
.3246753247 * 462 = 150 cubic inches.
30954 + 150 = 31104 cubic inches.
31104 / 36656 = 2/3 of a cubic yard.
a cubic yard weighs 1.5 tons.
2/3 * 1.5 = 1 ton.

everything checks out.
1 ton of sand fills 2/3 of a cubic yard of sand.
2/3 of a cubic yard is equal to 2/3 * 46656 = 31104 cubic yards.
31104 cubic yard / 462 cubic yards in an ammo box = 67 full ammo boxes plus an additional ammo box that is partially filled.

your solution is that 67 ammo boxes can be completely filled by 1 ton of sand.

i'm reasonably certain that this is correct.
check out the numbers and the logic to see if you agree.
if you don't, then let me know why and what you think the solution should be.