At a glassware factory, molten cobalt glass is poured into molds to make paperweights. Each mold is a rectanglar prism whose height is 3 inches greater than the length of each side of the square base. A machine pours 20 cubic inches of liquid glass into each mold. What are the dimensions of the mold?
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life orientation
To find the dimensions of the mold, we can use the given information about the volume of glass poured into each mold.
Let's assume that the length of each side of the square base of the mold is x inches.
According to the problem, the height of the mold is 3 inches greater than the length of each side of the square base. So the height of the mold would be (x + 3) inches.
The volume of a rectangular prism is calculated by multiplying the length, width, and height. In this case, the volume of the mold is given as 20 cubic inches.
Therefore, we have the equation:
Volume of the mold = x * x * (x + 3) = 20 cubic inches
Expanding the equation:
x^2 * (x + 3) = 20
Simplifying the equation:
x^3 + 3x^2 - 20 = 0
To solve the equation, we can try different values of x until we find a solution that satisfies the equation.
After trying different values, we find that x = 2 satisfies the equation:
2^3 + 3(2)^2 - 20 = 0
8 + 12 - 20 = 0
Therefore, the length of each side of the square base is 2 inches.
Now we can calculate the height of the mold:
Height of the mold = x + 3 = 2 + 3 = 5 inches
So, the dimensions of the mold are 2 inches by 2 inches by 5 inches.