To find out how many pyramids the artist can make from the block of alabaster, we need to follow a step-by-step approach:
1. Calculate the volume of one pyramid:
The formula for the volume of a pyramid is
[tex]\[
\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\][/tex]
Given:
- The base area is 3 square inches.
- The height is 4 inches.
Substitute these values into the formula:
[tex]\[
\text{Volume of one pyramid} = \frac{1}{3} \times 3 \text{ in}^2 \times 4 \text{ in}
\][/tex]
Simplifying inside the parentheses first:
[tex]\[
\frac{1}{3} \times 12 \text{ in}^3 = 4 \text{ in}^3
\][/tex]
So, the volume of one pyramid is 4 cubic inches.
2. Calculate the maximum number of pyramids that can be made:
The total volume of alabaster available is 576 cubic inches.
To find the number of pyramids that can be made, divide the total volume of the block by the volume of one pyramid:
[tex]\[
\text{Maximum number of pyramids} = \frac{576 \text{ in}^3}{4 \text{ in}^3} = 144
\][/tex]
Thus, the artist can make a maximum of 144 pyramids from the block of alabaster.
The correct answer is:
B. 144
