A glass box shaped like a rectangular prism has width 7 inches and height 12 inches it is being shipped in a larger box with width 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?
The length of the glass box is not provided, so we cannot determine the exact volume of the space between the two boxes. However, we can find the maximum volume of the space by assuming that the glass box is a cube with side length 7 inches (since this gives the maximum amount of space for the peanuts).
The volume of the glass box is then 7 x 7 x 12 = 588 cubic inches.
The volume of the shipping box is 10 x 15 x L, where L is the length of the glass box (in inches).
The volume of the space between the two boxes is therefore:
10 x 15 x L - 588
Simplifying this expression, we get:
150L - 588
Since we do not know the exact length of the glass box, we cannot calculate the exact volume of the space. However, we do know that it will be less than or equal to 150L - 588 cubic inches.
To find the cubic inches of space that will contain Styrofoam peanuts, we need to calculate the volume of the empty space between the glass box and the shipping box.
The volume of a rectangular prism is given by the formula: volume = length × width × height.
Since the length of the glass box is not provided, we can assume it is irrelevant for this calculation as it only affects the overall size of the box, not the empty space between the two boxes.
Let's calculate the volume of the empty space:
Empty space width = Shipping box width - Glass box width = 10 inches - 7 inches = 3 inches.
Empty space height = Shipping box height - Glass box height = 15 inches - 12 inches = 3 inches.
Now we can calculate the volume of the empty space:
Empty space volume = Empty space width × Empty space height × Length, where Length is assumed to be irrelevant.
Empty space volume = 3 inches × 3 inches × Length = 9 inches² × Length.
However, since we do not have the value of Length, we cannot calculate the exact volume. Without the length, we cannot determine the total amount of space that will contain Styrofoam peanuts.
To find the amount of space that will contain Styrofoam peanuts, we need to calculate the volume of the space between the glass box and the shipping box.
The length of the glass box is not given, so let's assume it has a length of L inches.
The volume of the glass box is given by length x width x height = L x 7 x 12 = 84L cubic inches.
The volume of the shipping box is given by width x height = 10 x 15 = 150 cubic inches.
The volume of the space containing Styrofoam peanuts is the difference between the volume of the shipping box and the volume of the glass box.
Volume of space = 150 - 84L cubic inches.
Therefore, the cubic inches of space that will contain Styrofoam peanuts is 150 - 84L.