Math Problem Statement
Solution
To solve this problem, we need to find the volume of the given right tetrahedron. A tetrahedron is a three-dimensional figure with four triangular faces. The formula for the volume of a tetrahedron with a right-angle vertex can be expressed as:
In the provided diagram, the tetrahedron has the right-angle vertex at point , with three labeled edges forming a right triangle. These labeled edges provide the base and height for our calculations.
The base triangle lies in the -plane, where:
- The edge along the -axis is 100 units.
- The edge along the -axis is 96 units.
These two edges form a right triangle, so the area of this triangular base is:
The height of the tetrahedron is along the -axis, which is 128 units.
Now, we can calculate the volume:
= \frac{1}{3} \cdot \frac{1}{2} \cdot 100 \cdot 96 \cdot 128$$ Let's compute this.The volume of the given right tetrahedron is $$204800$$ cubic units. Would you like a detailed breakdown of the steps, or do you have any further questions? Here are 5 related questions you may find helpful: 1. How do you calculate the volume of a general tetrahedron? 2. What are the properties of a right tetrahedron? 3. How is the volume of a pyramid related to the volume of a tetrahedron? 4. How can you use vectors to find the volume of a tetrahedron? 5. How do you find the surface area of a tetrahedron? **Tip:** Always make sure that the units for all dimensions are consistent before calculating volume or area in any problem!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Geometry
Solid Figures
Tetrahedron Volume
Formulas
Volume of a tetrahedron: V = (1/3) * Base Area * Height
Base Area of a triangle: A = (1/2) * base * height
Theorems
Volume of Pyramids and Tetrahedrons
Suitable Grade Level
Grades 9-12
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