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The volume of a truncated rectangular pyramidal pond 2016-05-13
From Paul:
How do you calculate a partially filled truncated rectangular pyramid if you always know the bottom rectangle, the maximum height top rectangle perimeter, but have a varying height. Similar to filling up a pond you know the current height and dimensions at the max rectangle how do you calculate it half full i.e. 10x30 outside perimeter with a 2x8 base and a max height of 6ft how do you calculate it at 3ft without re-measuring the top perimeter. Thanks, Paul
Answered by Harley Weston.
A frustum of a pyramid with a square base 2014-04-18
From tuba:
a pyramid has a base of 10 m and is 15 m high.what is the volume? if 6m is removed from top what is the volume of the remaining frustum?
Answered by Penny Nom.
The volume of a frustum 2014-02-02
From mike:
volume of frustum R23", r 18", h 16"
Answered by Penny Nom.
A frustum 2013-10-12
From Lily:
A cone of height 6in. and radius of base 4in. has its top cut off by a plane parallel to its base and 4in from it. Find the volume of the remaining frustum.

I have worked out the volume of the entire cone but I don't know how to work out the radius of the top of the frustum.


Answered by Penny Nom.
A label to cover a plastic cup 2012-10-23
From Kevin:
I'm trying to make a label to cover the entire outer area or a plastic cup. I know there must be a way to figure out the dimensions needed, but I can't seem to figure it out. The circumference of the bottom of the cup is 21.4cm and the circumference at the top of the cup is 29.8cm. The cup is 14.5cm tall. What should the height of the arc from the plane connecting the two ends of the 21.4cm arc. I attached a diagram where x is the value I'm looking for. I'm guessing there is some simple relationship between the length of a line and the arc needed to turn that line into a perfect circle, but I don't know what it is. Can you figure this out and share it with me? Thanks.


Answered by Penny Nom.
The volume of a frustum of a cone 2011-12-24
From CV:
If I know the height, taper, and volume of a frustum cone, what are its Radii?

Calculating frustum cone volume is straight forward.
v=Pi/3*h*(R*R+r*r+R*r) where;
h=frustum height;
R=major radius;
r=minor radius;
t=taper, ('slant angle' where t=0 is a disk)

Here is the tricky part.
Knowing 'h', 't', & 'v';
Calculate one or both of 'R' & 'r'.

Specifically, what is the formula for 'R=' or 'r='?

Answered by Penny Nom.
More on a truncated cone 2010-05-28
From Mike:

Question from Mike, a parent:

I was reviewing this question and answer:

But I have trouble with this part:
Now if we express the radius of the inside circle as r and the outside circle's radius is R, then this means r/R is 911/1728. But earlier we said that the outside radius R is simply w more than the inside radius r, so R = r + 282. That means that r/R = r/(r + 282). Now we can simply solve the equation for r:
r/(r+282) = 911/1728
This means r = 314 mm (with rounding).

Can I get more detail on the method to solve for r?

Thank you,

Answered by Penny Nom.
The volume of a frusta of a hexagonal based pyramid 2010-03-04
From sarah:
Volume of a frusta of a hexagonal based pyramid
Answered by Penny Nom.
The volume of a frustum 2009-12-29
From dave:
I have a frustum top 1.7r bottom .55r and 2.14 h I have to calculate cement in a silo every week. I am not very good at maths but i have been adding the top and bottom to get an average so as to turn it into a cylinder and i come up with 8.5m3 I know that the correct volume is 9.24 m3. Can you tell me why getting an average width on the top and bottom of a frustum doesn't work.
Thank you.

Answered by Chris Fisher.
Belled-out pier 2008-01-28
From Gina:
I need to know how to find the total yards needed to fill a concrete pier that is 54"/ 108" and 26' deep. That is...54" @ the top of the pier belled to 108" @ the bottom...26' deep.
Answered by Stephen La Rocque.
The volume of a frustum of a pyramid 2007-01-17
From Sam:
Find the volume of a frustum of a pyramid with square base of side b, square top of side a, and height h.
Answered by Penny Nom.
A Frustum 1999-03-29
From Monica Armour:
What do you call a square pyramid that has had the top chopped off?
Answered by Chris Fisher and Jack LeSage.



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