







The diameter of the top of a truncated cone 
20160124 

From Peter: I am trying to calculate the diameter of a truncated cone given
one diameter the height of the cone and a 10% taper from one end
to the other. For example a butter churn is 18" tall and 9" in
diameter at the base. the sides need to slope inward at 10%
What is the diameter at 9" and 18" Answered by Penny Nom. 





A label to cover a plastic cup 
20121023 

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.
Kevin Answered by Penny Nom. 





Making a wind sock 
20120828 

From John: I am trying to build a wind sock and need to be able to lay the shape
out on cloth. I need the wind sock front opening (diameter) to be
3 1/2" and the rear opening diameter to be 1". The windsock needs
to be 9 1/2" long. I tried using the example of the person trying to
make a crayfish trap but got confused and could not figure out my
numbers. Any help would be greatly appreciated.
Thanks
John Answered by Penny Nom. 





A tapestry rod on a curved wall 
20120814 

From Marlyn: I have a curved wall with a radius of 6'. I am trying to have a 36" rod made to hang a tapestry and need to figure out the degree measure of the arc.
Can you help me please? Answered by Penny Nom. 





A truncated cone: the central angle 
20120717 

From Tom: I have researched several sites, including this one and am fairly confident I can do the calculations required to produce the two radii and the slant height for a truncated cone.
I a somewhat confused by the central angle. Some sites indicate that it should never exceed 180 degrees while others do not. Different examples on your site seem to use this in two different ways in constructing a truncated cone.
Sometimes the angle seems to indicate the section to be removed, while in other examples the angle seems to indicate the section to be saved. Since the two angles will always total 360 I am confused about how to use the info to
calculate the minimum rectangle required to contain the pattern. I'm guessing that in some cases I may need to use the chord or sagitta to determine the desired height and width of the material. Any help is greatly appreciated.
Thank you.
Tom Answered by Penny Nom. 





A water tank is in the shape of a truncated cone 
20120308 

From Victoria: Suppose you have a water tank in the shape of a truncated cone. The larger diameter is K, the smaller diameter is K/2, and the height is also K (all measured in meters). The force of gravity on an object of mass, m, is F=9.8m (measured in Newtons). The density of the water is 1000 kilograms per cubic meter. What is the volume of the tank and how much mass will the tank have when it is full? Answered by Penny Nom. 





Making a truncated cone 
20110218 

From lisa: We need to make a cone that has the following dimensions.
143/8" diameter on large end
133/8" diameter on small end
4" tall
What are the dimensions I need to cut in order to make a cone with one seam? Answered by Stephen La Rocque. 





Calibrating a conical tank 
20110205 

From Bill: Hi, I have a round tank with tapered sides where I know the diameter at the top and bottom. Is there a formula I can use to calculate the volume by measuring from the bottom up the side (at the angle of the side) to any given point? Thanks, Bill Answered by Stephen La Rocque and Penny Nom. 





A 3D cardboard cupcake 
20100130 

From Margaret: Hi,
I'm an art student and I'm attempting to build a 3D cupcake out of cardboard.
I want it to have a circular base of 8.5 inches and sides that are 7'' tall and slope outward so the top of the base is 29'.
The top with the frosting would be a detachable lid made from a cone with a base circumfrance of 29".
My problem is how to cut the side so they will slope out, I'm pretty sure there needs to be a curve, however I don't how to calculate the degree of it.
Ideally I want the sides to be a single piece of cardboard.
I also don't know how to calculate the arc needed to make a cone who's circular base's circumfrence is 29''.
Thanks,
Margaret Answered by Stephen La Rocque. 





A truncated cone 
20091111 

From Lucian: I need to calculate the bottom inside diameter of a truncated cone.
The top insdie diameter is 1450mm.
The material is 6mm thick
The cone angle is 20 degrees
The slant length is 152mm
I would like a formula so that I can build a spread sheet Answered by Penny Nom. 





The volume of a telephone pole 
20090811 

From robert: 12.5"@ base x 7" @ top and 40' height. How would I find the volume in cubic feet for a telephone pole with these dimensions? Answered by Harley Weston. 





The volume of a tapered pole 
20090809 

From robert: what is the formula to use to come up with cubic feet in a tapered pole Answered by Harley Weston. 





The length of tape on a reel 
20090806 

From Philiip: What diameter reel would be required to roll up 1000 meters of tape that is 0.01 mm thick such that the final role left 10 mm empty space between the top of the roll and the outside of the reel, the hup that the tape was wound on was 2 cm? Answered by Stephen La Rocque. 





The dimensions of a larger cup 
20090523 

From Elizabeth: Hey
If i have a cup that holds a volume of 477mL and the bottom radius is 2.8cm and the top radius is 4.9cm and the height is 10cm. If i increase the volume by one and a half times what is the new measurements if the cup is directly proportional to the first one.
Thank you Answered by Stephen La Rocque and Penny Nom. 





Pattern for a truncated cone 
20070511 

From Mike: I have been trying to get this cone flat so I can build this column. Can you please help me so I can figure this out? Thanks for your help. Answered by Stephen La Rocque. 





Motorcycle expansion chamber design 
20061114 

From David: I'm interested in calculating cone information regarding motorcycle expansion chamber design for example. I guess it's called a truncated cone, from what I've read so far. If I know the center line height, small radius, and large radius of a truncated cone then, how can I calculate the angle (included angle?) the cone forms? I'd like to know the variations of the formula so I can calculate for angle, or length, or one of the diameters if I know the other two measurements. Answered by Stephen La Rocque. 





A truncated cone 
20060528 

From Phil: Hi, I am an art student and I am trying to make a "truncated cone" (ie: a cone with the top cut off) out of sheet metal. I need to design a template first and am having problems working out the angles. The truncated cone is 250mm high, 550mm wide at the bottom and 290mm wide at the top. Can you help? Answered by Stephen La Rocque. 





Tapes and CD's 
20001022 

From Arnold: Nicole has 25 CDs and tapes altogether. When she tries to pair them up, she has 4 CDs left over. How many tapes does Nicole have? Answered by Penny Nom. 

