Question

Adobe mud can be poured into molds to make bricks. Each brick is a rectangular prism with a width 4 inches less than its length and a height 6 inches less than its length. Each mold holds 576 cubic inches of mud. What are the dimensions of the mold?

Answer 1

Answer: Let's call the length of the brick "l". Then, the width is "l - 4" and the height is "l - 6".

The volume of the brick can be expressed as:

V = l * (l - 4) * (l - 6)

Since each mold holds 576 cubic inches of mud, we can set the volume of the brick equal to 576 and solve for l:

l * (l - 4) * (l - 6) = 576

Expanding and simplifying the left side of the equation, we get:

l^3 - 10l^2 + 24l - 576 = 0

This is a cubic equation, and finding the exact value for l can be difficult. However, we can use numerical methods, such as the bisection method or Newton's method, to find an approximate value.

Explanation: