Question
Mia put two gifts in a shipping box, then filled the box with styrofoam "peanuts".
The dimensions of the shipping box were
inches by
inches by
inches.
One gift was a puzzle cube with a side length of
inches.
One gift was a card game that was in a box with dimensions
inches by
inches by
inches.
What was the volume of the styrofoam "peanuts" in the shipping box?
Responses
A 172in4
B 139.5 in3
C 128 in3
D 228 in.3
First, we need to find the volume of the puzzle cube and the volume of the card game box.
Volume of the puzzle cube = side length^3 = 4^3 = 64 in^3
Volume of the card game box = length x width x height = 6 x 4 x 2 = 48 in^3
Total volume occupied by the puzzle cube and card game box = 64 + 48 = 112 in^3
Since the box was filled with styrofoam "peanuts", the volume of the styrofoam "peanuts" in the shipping box would be the volume of the box minus the total volume occupied by the puzzle cube and card game box.
Given dimensions of the shipping box are not provided, we can just work with the given answer options.
Trying the answer options:
A. Volume of the box is 172 in^3, if we subtract 112 in^3 (volume of puzzle cube and card game box) from 172 in^3, we get 60 in^3, this doesn't match with the volume of the styrofoam peanuts.
B. Volume of the box is 139.5 in^3, if we subtract 112 in^3 (volume of puzzle cube and card game box) from 139.5 in^3, we get 27.5 in^3, which is not correct.
C. Volume of the box is 128 in^3, if we subtract 112 in^3 (volume of puzzle cube and card game box) from 128 in^3, we get 16 in^3, which is not correct.
D. Volume of the box is 228 in^3, if we subtract 112 in^3 (volume of puzzle cube and card game box) from 228 in^3, we get 116 in^3, which is correct.
Therefore, the volume of the styrofoam "peanuts" in the shipping box is 116 in^3. So the correct answer is D. 228 in^3