Math Problem Statement
Solution
To solve the problem, let's denote the dimensions of the rectangular box as , , and . The areas of the three faces of the rectangular box are given as follows:
We are asked to find the volume of the box, which is .
Step 1: Multiply all the area equations
To eliminate the variables, multiply the three equations together:
Simplifying the left-hand side:
Now, simplify the right-hand side:
So, we have:
Step 2: Solve for the volume
To find , take the square root of both sides:
Thus, the volume of the box is .
Would you like further details on any step, or have any questions?
Here are five follow-up questions to explore further:
- What are the individual dimensions , , and of the box?
- How would the solution change if one of the given areas was different?
- Can you find the surface area of the box based on the given information?
- What is the geometric significance of multiplying the areas of the faces?
- How would you approach the problem if only two areas were given?
Tip: When solving for dimensions, multiplying related variables and simplifying equations can help eliminate unnecessary variables.
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Math Problem Analysis
Mathematical Concepts
Geometry
Volume
Rectangular Box
Formulas
Volume of a rectangular box V = x * y * z
xy = 30 cm², yz = 18 cm², xz = 15 cm²
(x * y * z)² = (xy)(yz)(xz)
Theorems
-
Suitable Grade Level
Grades 8-10
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