Math Problem Statement
Solution
Problem Analysis:
The problem involves a cuboid where:
- Length () is twice the breadth (): ,
- Height () is 10 cm: ,
- Total Surface Area (TSA): ,
- We are required to find the Volume of the cuboid.
Step-by-Step Solution:
1. Formula for Total Surface Area:
The TSA of a cuboid is given by:
Substitute and into the formula:
Set :
2. Simplify the Quadratic Equation:
Divide the equation by 4 to simplify:
3. Solve the Quadratic Equation:
Using the quadratic formula:
Substitute the values:
Choose the positive root:
4. Calculate Length:
Since :
5. Calculate Volume:
The Volume () of a cuboid is given by:
Final Answer:
The volume of the cuboid is:
Let me know if you'd like further details or clarifications! 😊
Related Questions:
- How is the total surface area formula derived for a cuboid?
- What is the general method for solving quadratic equations?
- How would the solution change if the height were doubled?
- Can we verify the calculations using unit consistency?
- What happens to the volume if all dimensions are doubled?
Tip:
Always cross-check dimensions (units) when solving geometry problems to ensure consistency!
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Math Problem Analysis
Mathematical Concepts
Geometry
Quadratic Equations
Volume
Total Surface Area
Formulas
Total Surface Area (TSA) of a cuboid = 2(lb + bh + hl)
Volume of a cuboid = l × b × h
Quadratic equation formula: ax² + bx + c = 0
Theorems
Quadratic Formula
Suitable Grade Level
Grade 8-10
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