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. 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?a. 2 ft.b. 4 ft.c. 6 ft.d. 8 ft.

Answer 1

Answer:

d. $8\text{ ft}^3$

Step-by-step explanation:

We have been given that Cheng measures each edge of each base to be 2 feet. The height of the whole sculpture is 6 feet.

First of all, we will find height of each pyramid by dividing height of whole sculpture by 4 as:

$\frac{6\text{ ft}}{4}=1.5\text{ ft}$

We know that volume of a pyramid is equal to 1/3 of base area times height that is $V=\frac{bh}{3}$, where b represents area of base.

$V=\frac{(2\text{ ft})^2\times\text{ 1.5 ft}}{3}=4\times 0.5\text{ ft}^3=2\text{ ft}^3$

Since volume of one pyramid is equal to 2 cubic feet, so volume of 4 pyramids will be 4 times 2 cubic feet that is 8 cubic feet.

Therefore, Cheng must purchase 8 cubic feet of material.