Math Problem Statement
Solution
In this problem, we are given the dimensions of an open box, and the task is to write a quadratic equation to find the unknown dimension , given that the volume of the box is 182 cubic centimeters.
Step 1: Understand the box dimensions
- The length of the base is .
- The width of the base is .
- The height of the box is 2 cm (as shown by the folded sides).
Step 2: Write the formula for the volume of a rectangular box
The formula for the volume of a rectangular box is:
Using the dimensions from the diagram:
- Length =
- Width =
- Height =
The volume equation becomes:
Step 3: Substitute the given volume
We are told that the volume is 182 cubic centimeters, so:
Step 4: Simplify the equation
First, divide both sides by 2 to simplify:
Now, expand the left-hand side:
Step 5: Form the quadratic equation
Rearrange the equation to standard quadratic form:
This is the quadratic equation that can be used to solve for .
Would you like details on solving this quadratic equation, or any other questions on this topic?
5 Related Questions:
- How can you solve the quadratic equation ?
- What are the possible values of once the quadratic equation is solved?
- How does the box's volume change if the height is doubled?
- What is the relationship between the volume and the surface area of the box?
- Can you use the quadratic formula to solve this type of box dimension problem?
Tip:
When expanding or simplifying expressions, always check for common factors to reduce the equation before solving. This helps avoid mistakes and simplifies the process!
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Volume of Rectangular Prisms
Formulas
Volume of a rectangular box: V = length × width × height
Standard form of a quadratic equation: ax^2 + bx + c = 0
Theorems
Expansion of binomials
Rearranging equations to standard form
Suitable Grade Level
Grades 8-10
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