How many Dice fit in a box problem

[Colevisc11]

I have tried to find this question out but didn't know whether it was 40 or 2560
Mr. Yahtzee needs more dice to complete his game collection. The dice are each 1/2 in by 1/2 in by 1/2 in. How many dice can fit in a box he was sent from Amazon that is 10 inches long, 4 inches wide and 8 inches high?

Work:
1/2 times 1/2 times 1/2 is 1/8
10 times 4 times 8 is 320

Or

320 times 1/8 is 40
320 divided by 1/8 is 2560

 

[Deleted member 4993]

I have tried to find this question out but didn't know whether it was 40 or 2560

Mr. Yahtzee needs more dice to complete his game collection. The dice are each 1/2 in by 1/2 in by 1/2 in. How many dice can fit in a box he was sent from Amazon that is 10 inches long, 4 inches wide and 8 inches high?

How did you get those numbers?

Please show work.

 

[Colevisc11]

Dice in a box

I have tried to find this question out but didn't know whether it was 40 or 2560

Mr. Yahtzee needs more dice to complete his game collection. The dice are each 1/2 in by 1/2 in by 1/2 in. How many dice can fit in a box he was sent from Amazon that is 10 inches long, 4 inches wide and 8 inches high?

Work:
1/2 times 1/2 times 1/2 is 1/8
10 times 4 times 8 is 320

Or

320 times 1/8 is 40
320 divided by 1/8 is 2560

 

[Ishuda]

I have tried to find this question out but didn't know whether it was 40 or 2560
Mr. Yahtzee needs more dice to complete his game collection. The dice are each 1/2 in by 1/2 in by 1/2 in. How many dice can fit in a box he was sent from Amazon that is 10 inches long, 4 inches wide and 8 inches high?

Work:
1/2 times 1/2 times 1/2 is 1/8
10 times 4 times 8 is 320

Or

320 times 1/8 is 40
320 divided by 1/8 is 2560

In this particular case, this will work [using the divided by] because the dice fit exactly into the given volume. But what if the box had been 10.25 by 4 by 8. That would give a volume of 328 which, when divided by the 1/8 would give 2624 while, in reality, the answer would still be 2560.

In addition, using units can help you decide whether to multiple or divide. You have
1 dice = 1/8 cu in
or
8 dice = 1/(1/8) dice = cu in.
1 box = 320 [cu in] = 320 * [8 dice] = 320 * [1/(1/8) dice]