Question

Cheng likes a modern lawn sculpture made of four identical solid right pyramids with square bases. He decides to create an exact copy of the sculpture, so he needs to know what volume of sculpting material to purchase.

2 identical solid right pyramids with square bases are connected at the square base. Another 2 are connected in the same way and are stacked on top of the other 2 pyramids. The length of the base edge is 2 feet and the height of the whole structure is 6 feet.

He measures each edge of each base to be 2 feet. The height of the whole sculpture is 6 feet.

What is the volume of material he must purchase?

2 ft3
4 ft3
6 ft3
8 ft3

Answer 1

Each pyramid has base area 2^2 = 4 ft^2. Let the height of one pyramid be h. Two glued base-to-base make height 2h; stacking two such pairs gives total height 4h = 6, so h = 1.5 ft.

Volume of one pyramid = (1/3)(base area)(height) = (1/3)(4)(1.5) = 2 ft^3. For 4 pyramids: 4·2 = 8 ft^3.

Answer: 8 ft^3.