Math Problem Statement
Solution
The problem provided involves a triangular prism with the following known values:
- Height (h) = 8 cm
- Volume (V) = 216 cm³
The formula for the volume of a triangular prism is given as:
Where:
- is the volume of the prism,
- is the area of the triangular base, and
- is the height of the prism.
We need to find the area of the base . To do so, we rearrange the formula to solve for :
Substituting the known values:
Thus, the area of the base of the triangular prism is 27 cm².
Would you like more details or have any questions?
Here are 5 related questions to expand on this:
- How do you find the volume of other types of prisms, like rectangular prisms?
- What is the formula for finding the area of a triangle?
- How can you determine the side lengths of the triangular base if only the area is given?
- How does the shape of the base affect the volume calculation for different prisms?
- What is the difference between surface area and volume?
Tip: Always keep track of units when solving geometry problems. Make sure to match units for volume, area, and length when substituting values into formulas!
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Math Problem Analysis
Mathematical Concepts
Geometry
Volume of Prisms
Area of Triangles
Formulas
Volume of a triangular prism: V = B × h
Area of base B = V / h
Theorems
Prism Volume Formula
Suitable Grade Level
Grades 6-8
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