Volume of a Truncated Pyramid (Frustrum volume)-MooMooMath

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Directions for finding the volume of a truncated pyramid. (frustum)
Basically a pyramid with the top cut off.

To find the volume of a truncated pyramid use 1/3 base x height of a pyramid and then subtract the portion of the pyramid that is missing.
1/3Bh-1/3Bh but the base and height measurements will be different.
The base areas are pretty easy to find because they are given.
The altitude is a little tricky, but can be solved by setting up proportions in order to find slant height..
Next, I use the Pythagorean Theorem with the slant height in order to find the altitude.
I will repeat this for the smaller base.
Finally I will plug all of these dimensions in
1/3Bh-1/3Bh for the volume of the truncated pyramid.

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[hasiearth]

What about irregular frustum?
For Ex. Bottom rectangle with dimension 2.75mx2.2m, hight 0.6m, top rectangle with side dim 0.4mx0.95m, and line joining centres of rectangle vertically inclined at an angle 10 degree.

[kmasood]

A pyramidal frustum is a frustum made by chopping the top off a pyramid. It is a special case of a prismatoid.


For a right pyramidal frustum, let s be the slant height, h the height, p_1 the bottom base perimeter, p_2 the top base perimeter, A_1 the bottom area, and A_2 the top area. Then the surface area (of the sides) and volume of a pyramidal frustum are given by


S = 1/2(p_1+p_2)s
(1)
V = 1/3h(A_1+A_2+sqrt(A_1A_2)).

[ajaychavada]

But how to find the volume if we dont know the value of the cutted portion and we do not have the entire height and we do not have square but rectangular shape at top as well as bottom....???

[Melvorgazh]

Hello,
What is the formula of the volume of a truncated decagonal pyramid, please?
Regards and thanks,
Thomas

[gianchristianlim]

Can we use 5 and 3 as the sides of the right triangle to determine the height?

[utube]

I dont know how my teacher did this but .she did ( 10 ^2+ 6^2+4×8^2)/6 ie: she took total surface area of the question and averaged it by dividing with 6. Side with dimension 8 is (6+10)/2 for the curved sides . Now she multiplied that average area with the height of cut cone (18.7-11.2) .
U should get 65.33×7.5 which gives 490.
If u dont take rounded off digits in above calculation i think u will get same results in both both.

[mohammadahmed]

How can we calculate volume of frustom of pyramid in excel .thanks

[sisikelelwemadikani]

Why height of bottom height is not 18.71-11.72

[banerjeefamilycreation]

What is your country, I am from India

[LOPGOH]

Tetrahedron 🤔3 Sided Pyramid or 4? This helped. But I was reading comments...

I know it's self evident. Just needed a sec

[tribunic]

how or where did you get the 4x=48 and x=12?

[kmasood]

it's FRUSTUM NOT FRUSTRUM
there's no "r"
get it right 🙄