Bridget bought a glass pyramid from a gift store. The pyramid, with a height of 4 cm and a square base of side 6 cm, was packed in a box shaped as a cube of side 7 cm. The empty space in the box was packed with paper tissue. How many cubic centimeters of the box were stuffed with paper tissue?

Question

Bridget bought a glass pyramid from a gift store. The pyramid, with a height of 4 cm and a square base of side 6 cm, was packed in a box shaped as a cube of side 7 cm. The empty space in the box was packed with paper tissue.    How many cubic centimeters of the box were stuffed with paper tissue?

anonymous · Answer

please help me

blacksteel · Answer

Okay, to solve this problem you need to find the total volume of the box, then remove the portion of that volume that's filled by the pyramid.

The box is a cube; the equation for the volume of a cube with side length s is s^3. Since the side length in this case is 7 cm, the volume of the cube is (7 cm)^3, or 343 cc. (cc is cubic centimeter).

The volume of a pyramid is given by the formula V = (1/3)b*h, where b is the area of the pyramid's base and h is the height of the pyramid. In this case, h = 4 cm and the area of the base is going to be the area of a square with side length 6 cm, so it's (6 cm)^2, or 36 cm^2.
Then the volume is (1/3)*(4 cm)*(36 cm^@) = 48 cc.

Then the volume taken up by the tissue paper is the volume of the box minus the volume taken up by the pyramid, 343 cc - 48 cc = 295 cc