a storage crate has the dimensions : 12ft * 6ft *5ft. how many cube-shaped boxes measuring 8 inches in length could be stacked completely within the cube??
To determine the number of cube-shaped boxes that can be stacked completely within the given storage crate, let's first convert the dimensions of the crate from feet to inches:
Length of the crate: 12ft * 12in/ft = 144 inches
Width of the crate: 6ft * 12in/ft = 72 inches
Height of the crate: 5ft * 12in/ft = 60 inches
Now, let's find out how many of these 8-inch cube-shaped boxes can fit in each dimension:
Number of boxes along the Length: 144 inches / 8 inches = 18 boxes
Number of boxes along the Width: 72 inches / 8 inches = 9 boxes
Number of boxes along the Height: 60 inches / 8 inches = 7.5 boxes
Since the height does not allow for a whole number of boxes, we have to round down to the nearest whole number. Therefore, we can stack a total of 18 boxes along the length by 9 boxes along the width by 7 boxes along the height.
To find the total number of boxes, we can multiply the number of boxes in each dimension:
18 boxes * 9 boxes * 7 boxes = 1,134 cube-shaped boxes.
Therefore, we can stack a total of 1,134 cube-shaped boxes measuring 8 inches in length completely within the given storage crate.