Math Problem Statement
Solution
To solve the problem:
Step 1: Formula for the volume of a pyramid
The formula for the volume of a pyramid is:
Step 2: Find the base area
The base of the pyramid is a rectangle with dimensions 12 cm × 8 cm. The base area is:
Step 3: Substitute the given volume
The volume of the pyramid is 544 cm³. Substitute into the formula:
Step 4: Solve for height
Rearrange the formula to solve for :
Simplify:
Final Answer:
The perpendicular height of the pyramid is:
Would you like additional clarification or more details on the calculation steps?
Here are 5 related questions to consider:
- How do you calculate the volume of a triangular-based pyramid?
- What happens to the volume if the height doubles?
- How can you find the height if the base is irregularly shaped?
- Why is the factor used in the pyramid volume formula?
- How would this problem change if the base was a triangle instead of a rectangle?
Tip: Always double-check your unit conversions to ensure accuracy when solving geometric problems!
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Math Problem Analysis
Mathematical Concepts
Geometry
Volume of a Pyramid
Rectangular Base
Formulas
Volume of a Pyramid: V = (1/3) × Base Area × Height
Theorems
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Suitable Grade Level
Grades 7-10
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