Geometric calculations

Question

A safe in the shape of a cube is 2 feet on a side. The bank in which it is located stores bound stacks of cashed checks; each stack is 6 inches long, three inches wide , and three inches high. What is the maximum number of stacks that can be stored in this safe?

Answer 1

The stacks can be laid on the "floor" in a 4 x 8. That is 32 stacks.

Eight layers can be laid. That is 8 x 32 or 256 stacks.

 

Answer 2

FIND THE VOLUME OF THE SAFE:

 

    The safe is a cube ... each side is 2 feet ... or 24 inches.

    The volume of the cube is (24 in)³ = 13824 in³

 

FIND THE VOLUME OF EACH CASH STACK:

 

    Each stack is 6 in x 3 in x 3 in ... = (6)(3)(3) = 54 in³

 

To determine the number of stacks that can be stored in the safe, we divide.

 

    13824  in³ ÷ 54 in³ = 256

 

Thus 256 cash stacks can be stored in the safe.

 

 

Answer 3

Safe is two feet on each side, making its dimensions(inches):

 

24 in. by 24 in. by 24 in.

 

Each stack of checks is 6 in. by 3 in. by 3 in.

 

Lengthwise: 24 in. ÷ 6 in. = 4 stacks lengthwise

 

Widthwise: 24 in. ÷ 3 in. = 8 stacks across the width

 

Heightwise: 24 in. ÷ 3 in. = 8 stacks high

 

Therefor you have: 4 times 8 times 8 = 256 stacks of checks in safe 

Answer 4

We have to assume that the 2³f³ volume is the interior space of the safe. If it wasn't, the problem would be unsolvable because it doesn't specify the thickness of the safe's hull. So how many stacks of checks can fit in a 2³f³ volume?. We can start on any dimension we want. Let's start by calculating how many stacks can fit on top of each other. They are three inches high. The safe is 24in on every measurement (12in/f × 2f). So the maximum that can fit bottom to top is eight. They are three inches wide so for how many can fit when placed side by side, the the answer again is eight. They are six inches long. 24 inches divided by six inches is four. So you can fit four stacks end to end. to fill the whole safe, you will pack the stacks in a 8 by 4 by 8 arrangement. Now multiply the numbers. 8in × 4in × 8in = 256in³

 

Another way to approach this is to simply divide the volume of the safe by the volume of a stack. The volume of the safe is 13,824in³ (24³in³). The volume of a stack is 54in³ (3in × 3in × 6in). 13824in³ ÷ 54in³ = 256.