4. To solve this problem, we must simply subtract the volume of the smaller box from the volume of the larger box. The formula for volume of a rectangular prism is length * width * height. So we know that the bigger box has a height of 20 inches, a length of 15 inches, and a height of 9 inches. We can multiply these together to get the volume.
20 * 15 = 300
300 * 9 = 2700
The bigger box has a volume of 2,700 cubic inches.
Now for the smaller box. This box has a length of 12 inches, a width of 8 inches, and a height of 4 inches. Let us multiply this together:
12 * 8 = 96
96 * 4 = 384
The smaller box has a volume of 384 cubic inches.
Now, we just need to subtract.
2700 - 384 = 2316
There are 2,316 cubic inches of space left in Jeff's bigger box.
5. Mrs. Nelson has plans for a flower box that has two constant sidelengths, the length and height (5 feet and 2 feet). The width can be any whole number (counting number) only up to 5 feet, so there are 5 different volumes she could have. Those are:
5 * 2 * 1 = 10 cubic feet
5 * 2 * 2 = 20 cubic feet
5 * 2 * 3 = 30 cubic feet
5 * 2 * 4 = 40 cubic feet
and
5 * 2 * 5 = 50 cubic feet
The possible volumes for Mrs. Nelson's flower box are 10, 20, 30, 40, and 50 cubic feet.
