Math Problem Statement
Find the volume of the figure when b = 4 ft and h = 6 ft.
ft3
Solution
The image depicts a square pyramid, with the base having side length and height .
The formula to find the volume of a pyramid is:
For a square base, the base area is given by:
Substituting into the volume formula:
Given and :
Thus, the volume of the pyramid is 32 cubic feet.
Would you like more details or have any other questions?
Here are some follow-up questions to deepen understanding:
- How does the volume formula change for other types of pyramids?
- What would happen to the volume if the height doubled but the base stayed the same?
- How is the formula for a cone's volume similar to that of a pyramid?
- What is the significance of the factor in the volume formula?
- How would you calculate the surface area of this pyramid?
Tip: When dealing with pyramids, always verify the base shape and dimensions before applying the volume formula.
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Math Problem Analysis
Mathematical Concepts
Geometry
Solid Figures
Pyramids
Formulas
Volume of a Pyramid: V = (1/3) * Base Area * Height
Base Area for Square Pyramid: A = b^2
Theorems
Volume theorem for pyramids and cones
Suitable Grade Level
Grades 6-9
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