A glass box shaped like a rectangular prism has width 7 inches, length 9 inches, and height 12 inches. It is being shipped in a larger box with width 10 inches, length 10 inches, and height 15 inches. The space between the glass box and the shipping box will be filled with Styrofoam peanuts. How many cubic inches of space will contain Styrofoam peanuts? Show all work.
The volume of the glass box is:
$7\times 9\times 12 = 756$ cubic inches.
The volume of the shipping box is:
$10\times 10\times 15 = 1500$ cubic inches.
So the difference in volume (which is the amount of space the Styrofoam peanuts will occupy) is:
$1500-756=744$ cubic inches.
Therefore, 744 cubic inches of space will contain Styrofoam peanuts.
To find the space that will contain Styrofoam peanuts, we need to first calculate the volume of the glass box and the volume of the shipping box.
The volume of a rectangular prism (such as the glass box) is calculated by multiplying its length, width, and height.
Volume of glass box = length * width * height
= 9 inches * 7 inches * 12 inches
= 756 cubic inches
Similarly, the volume of the shipping box is calculated by multiplying its length, width, and height.
Volume of shipping box = length * width * height
= 10 inches * 10 inches * 15 inches
= 1500 cubic inches
Now, to find the space between the glass box and the shipping box (which will be filled with Styrofoam peanuts), we need to subtract the volume of the glass box from the volume of the shipping box.
Space for Styrofoam peanuts = Volume of shipping box - Volume of glass box
= 1500 cubic inches - 756 cubic inches
= 744 cubic inches
Therefore, 744 cubic inches of space will contain Styrofoam peanuts.