Math Problem Statement

An open box is to be made from a square piece of material 36 cm on a side by cutting equal

squares with a length of x from the corners and turning the sides up.

Solution

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Math Problem Analysis

Mathematical Concepts

Geometry
Optimization
Volume of a Box

Formulas

Volume of a box: V = length × width × height
Length and width after cutting: 36 - 2x
Height of the box: x
Volume formula: V(x) = (36 - 2x)^2 * x

Theorems

Maximization of a quadratic function

Suitable Grade Level

Grades 9-11