Question

an artist wants to make alabaster pyramids using a block of alabaster with a volume of 576 cubic inches. she plans to make each pyramid with a square base area of 3 square inches and a height of 4 inches. at most, how many pyramids can the artist make from the block of alabaster?
a. 136
b. 144
c. 154
d. 166
e. 172

Explanation:

Step1: Calculate the volume of one pyramid

The volume formula for a pyramid is \(V=\frac{1}{3}Bh\), where \(B\) is the base area and \(h\) is the height. Given \(B = 3\) square inches and \(h=4\) inches.

$$V=\frac{1}{3}\times3\times4$$

$$V = 4$$

cubic inches.

Step2: Calculate the number of pyramids

Divide the total volume of the alabaster block by the volume of one pyramid. The total volume of the alabaster block is \(576\) cubic inches.

$$n=\frac{576}{4}$$

$$n = 144$$

Answer:

B. 144