Aglass 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.

744 in³

Step-by-step explanation:

Since you are filling the larger box with both rectangular prism and Styrofoam peanuts, you need to find the overall volume of the larger box and subtract the volume of the glass box to find the amount of space that the Styrofoam peanuts need to take up.  

Volume (prism) = Bh, where B = area of the base, h = height

Larger Box:  V = 10 x 10 x 15 = 1500 in³

Glass Box: V = 7 x 9 x 12 = 756 in³

1500 - 756 = 744 in³ of Styrofoam peanuts

the arc length is found by finding the circumference of the full circle (2xpixradius) and then dividing by 4 to find just one quarter of the circle (90 degrees).