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How do you calculate the volume of a pyramid that has no top ie that has a large square base and a small square top?
Wiki User
∙ 11y ago
You calculate the volume of a pyramid by multiplying one third of the base area by the perpendicular height.
1/3 Area of base x Height
Depending on what you know of the pyramid, one of these methods determines the volume.
Method 1:
- Calculate the volume of the whole pyramid including the missing piece at the top (which is a small pyramid by itself)
- Calculate the volume of the small missing pyramid.
- Subtract the small volume of the small pyramid (step 2) from the volume of the large pyramid (step 1)
Method 2:
The difficulty for the above described method may be to determine the height of the pyramid in both step 1 and step 2. If you only know the height of the base till the top square, you can use the formula below to directly calculate the volume.
Assume the base is a * b and the small square on top c * d, with a and c on the same side (also for b and d). The height of the pyramid (from base to small square on top) is h.
We can split the top-off-pyramid in nine pieces. A block from top square to base, four pieces directly adjacent to this block and four corner pieces. This nice thing about this splitting is that we can form four new shapes from which we can easily determine the volume. The corner pieces together form a whole pyramid, 2 pieces adjacent to the block in 1 direction form a prism, as well as the other two and we have a rectangular block. I.e. we can form four new shapes of which we know the bases and the heights.
The volume of a prism is 1/2 Area of triangle * length
1. Assign a and b to the base sides and c and d to their corresponding top sides.
2. The volume of the top-off-pyramid will be (after simplification):
Volume of Block + Volume of pyramid + Volume of prism1 + Volume of prism2 =c d h+ 1/3 * h (a - c) * (b - d)
+ 1/2 * h (a - c) * d
+ 1/2 * h (b - d) * c--------------------------------1/3 h (a b + 1/2 a d + 1/2 b c + c d)
This formula shows that when c and d are 0, we will get the original pyramid formula back.
Wiki User
∙ 11y ago
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HttpwikianswerscomQHow do you caluclate the volume of a pyramid that has no top IE that has a large square base and a small square top?
you calculate the pyramid then deduct the portion you dont want
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