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A pattern for a truncated cone 2013-12-20
From Josh:
I need to know how to layout a truncated cone with a base diameter of 18" a top Diameter 15.25 and a height of 20". Your help will be greatly appreciated.
Answered by Penny Nom with a spreadsheet by Don.
Pattern for a truncated cone 2007-05-11
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.
A sand castle in the shape of a truncated cone 2020-05-23
From Summer:
A sand castle is in the shape of a truncated cone as shown. Calculate the length of the diameter of the base.
The diameter of the top of the truncated cone is 20cm
The height is 30cm
The slopes are 32cm

Answered by Penny Nom.
Running in opposite directions around a circular track 2020-05-11
From Alessandra:
2. Alan and Brian are two runners. Alan runs at 6.6 m/s and Brian runs at 8.4 m/s. They start from the same place on a circular 400 m track and run in opposite directions round and round the track.
(a) How far has Brian run when they pass each other for the first time?
(b) After they pass each other for the second time, how much further does Brian need to run in order to complete two laps (800 m)?

Answered by Penny Nom.
The missing diameter of a truncated cone 2020-04-17
From Brandon:
Need a formula to find missing large Dia of a truncated cone where the small dia =.19" Height= 2" and taper =16deg
Answered by Harley Weston.
The volume of a coffee cup 2020-01-25
From Amirah:
What is the volume of a polystyrene cup with a height of 8cm, diameter of 5cm at the top and 4cm at the bottom when it is filled with water?
Answered by Penny Nom.
Volume of a tree 2019-12-19
From Maria:
I have trees for sale. I need to calculate the volume of a tree from base which is wider than the stem.The base will be used for the making of hurleys, similar to hockey sticks so the wider base is crucial.
Answered by Penny Nom.
A flat top cone 2019-08-25
From Mary:
I want to make a paper model of a flat top cone with the radius of the base is 12.5 cm and the radius of the apex is 7 cm.The height is 15 cm and the radius of the apex is 5 cm. The height is 15 cm.
Can you help me with the angle and construction, please?

Answered by Penny Nom.
The top of a truncated cone 2018-12-02
From Sameer:
Bottom cone radius 1124.height is 200. Top radius 15degree decree to bottom radius. Top radius how much ?
Answered by Penny Nom.
Amy and Joey on a circular track 2018-08-13
From Zoe:
Amy and Joey are situated on a circular track 400 feet around.
Joey starts running at a rate of 10 feet per second.
Amy waits for a full minute, then starts running from the same point (in the same direction) at 12 feet per second.

How many seconds elapse before Amy passes Joey on the track?

Answered by Penny Nom.
Truncated cones 2018-08-08
From Belgacem:
Hello, I have a truncated cone: height 500mm , Base radius=147mm and I want to calculate the Top surface radius. How to do that? thank you
Answered by Penny Nom.
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.
The diameter of the top of a truncated cone 2016-01-24
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.
The height of a truncated cone 2015-12-04
From Jack:
I need to build a truncated cone that has a top of30 inches and a base of 64 inches . The sides need to be at a 64.5 degree angle. This will determine the height. Can this be calculated?
Answered by Penny Nom.
A truncated square-based pyramid 2014-10-22
From Beth:
How do you find the height of the original square-based pyramid when given the sides (12cm) of the base and height (6cm) of the truncated pyramid, as well as the sides (3cm) of the base of the chopped off top (chopped off parallel to the base)?
Answered by Penny Nom.
The volume of a pond 2013-08-14
From Kelly:
I have a pond that measures 335 feet wide, 385 feet long and 18 feet deep with a 4:1 slope on all four side. How do I figure out how many gallons of water this pond will hold?
Answered by Harley Weston.
Stairs for the new community center, part 2 2012-11-13
From Emily:
Plans for a set of stairs for the front of a new community center use the ratio of rise to run of 2 units to 5 units.

B. Sketch a set of stairs that meets the rise-to-run ratio of 2 units to 5 units.

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.
Making a wind sock 2012-08-28
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.



Answered by Penny Nom.
A truncated cone: the central angle 2012-07-17
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 lamp shade 2012-05-15
From Fleur:
I am helping my child make a cone lampshade, the measurements are as follows in "cm's"
21 cm = height
8 cm = top diametre
40 cm = bottom diametre

Please could you give the pattern (cut out) dimensions for final cut.

Answered by Penny Nom.
Cycling and running 2012-05-07
From liz:
a biathlete travels 20 miles in 2.25 hours. She cycles part of the way at 12 mph and runs the rest at 5 mph. How far did she run?
Answered by Penny Nom.
A water tank is in the shape of a truncated cone 2012-03-08
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.
A 23 acre airport runway 2012-02-21
From Ron:
I have a 23 acre plot. If it were in a straight line, would it be enough distance for a plane to take off and land if the plane needed 1 mile?
Answered by Robert Dawson and Penny Nom.
Running 5 km 2012-01-12
From Fayeann:
What amount of time will it take a person running 7 m/s to travel a distance of 5 km?
Answered by Penny Nom.
Building a custom range hood 2011-10-08
From Bill:
I'm building a custom range hood for a customer with special order material that matches their newly installed cabinets and I need it to be perfect. The hood is basically a pyramid but the 4th side is the flat wall at the back and a flat, rectangular top. I need to calculate the bevel and miter of the three sides but I never was very good with geometry functions (although I am fairly good with other math fields). I either need the calculations from you at least (shudder) a formula or set of formulas so that I can calculate them myself.
Answered by Harley Weston.
The volume of a hopper 2011-04-13
From michael:
I have a tank that is 72" x 72" at the top and 10" x 10" at the bottom and is 31" tall. I need to calculate the cubic feet of the tank
Answered by Penny Nom.
The volume of a flower pot 2011-04-07
From kp:
I have 2 flower pots with the following dimensions that I am trying to calculate the volume of Soil I will need to fill them. pot #1 29"tall, top of pot 31.5 inches across( radius of 15.5") the bottom of the pot is 21"across (radius 10.5) Pot #2 29"tall, top of pot 26 across (radius 13") the bottom of the pot 17'"a cross (radius 8.5")
thank you

Answered by Penny Nom.
New Brunswick hst 2011-03-25
From andy:
what is the short formula to get the hst 13% out of the total price of an item
Answered by Penny Nom.
Making a truncated cone 2011-02-18
From lisa:
We need to make a cone that has the following dimensions.
14-3/8" diameter on large end
13-3/8" 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 2011-02-05
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 truncated cone 2010-12-31
From jagjeet:
dear suppose i have cone of 50cm radius at base and 100cm radius at top at a height of 80cm. now keeping base radius of 50cm and height of 80cm i want to increase top radius to 150cm how will i do that. plz height m talking abt is vertical height not slant height
Answered by Penny Nom.
The volume of a truncated pyramid 2010-10-12
From A:
what is the formula to find out volume of a pyramid with individual length and breadth? For example bottom size is 6.5m x 6.5m, top size 1.5m x 4.2m and height 0.8m. please send me the formula.
Answered by Stephen La Rocque.
Volume of a styrofoam cup 2010-06-23
From Stacy:
how do you find the volume of a truncated cup with height of 3, top diameter of 2.5, and a bottom diameter of 2
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.
A 3D cardboard cupcake 2010-01-30
From Margaret:
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''.

Answered by Stephen La Rocque.
Truncated Octagonal Prism 2009-12-26
From freitas:
the top plane of the truncated octagonal right prism is 45 degree with respect to horizontal. find the volume
Answered by Janice Cotcher.
A truncated cone 2009-11-11
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 2009-08-11
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.
A cone with the top cut off 2009-08-02
From Paul:
I am making a cone with a diameter of 1300, a base of 500, a side length 800. I need to workout so I can draw it out flat, cut it out, and make into a cone.
Answered by Harley Weston.
The dimensions of a larger cup 2009-05-23
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.
12 oz. cup 2009-04-19
From Tom:
I am a ceramic teacher and wanted my students to make a 12 oz. cup, what formula should we use?
Answered by Chris Fisher.
A truncated tetrahedron 2009-02-05
From Brad:
If you take a regular tetrahedron and truncate it so you keep the original three 60degree angles around one vertex but the legs originating from it become any three consecutive terms of the Fibonacci series the new base is one triangle of a pentagon. I want to know the height of the new pyramid relative to its new base and the angles between the base and the other three sides.
Answered by Robert Dawson.
The volume of a feed hopper 2008-12-18
From John:
I need to calculate the volume of a feed hopper, and I'm not sure how to break it down. The top of the hopper is 36" x 36", it is 30" deep, and ends at a 6" x 6" plate. One side of the hopper is straight top to bottom, of course tapering on two sides to meet at the plate. The other three sides angle down at about 75 degrees. I need to determine the cubic foot volume of this hopper (it is used for ground coffee) so I can configure a vibrator to knock down residual grounds. Thanks.
Answered by Robert Dawson.
The volume of a cyclone 2008-11-13
From Dianna:
I need to figure the cubic yards of a cyclone. 144" down to 48" 60" high
Answered by Penny Nom.
An irregular, truncated pyramid 2008-10-24
From phillip:
Hi, I have a rectangular base to square top, pyramid shape to fabricate out of steel plate (4 sections). The base is 3000mm by 800mm, the height is 1100mm and the top is 350mm square. What I need to know is the lengths of the sides of the plate(were they meet vertically). Hope ive made it clear enough. Thanks Phil.
Answered by Stephen La Rocque.
The rise over the run 2008-10-07
From Mak:
what is the ratio of the rise to run?
Answered by Penny Nom.
A cardboard spaceship 2008-08-31
From Lee:
I am building a "cardboard" spaceship for my 4 year old grandson. The cabin is a dishwasher box with a cool control panel and elipse shaped windows. I really need help designing the cone or"nosecone". The diameter of the base is 26", 24" tall, with a 6" diameter opening at the top. Thank you for the help! Lee
Answered by Penny Nom.
A truncated cone 2008-04-11
From jason:
i need to know how to figure the cubic feet of a cone that the top is 72" wide the bottom is 25" wide and it is 48" tall. is there a specific formula for this?
Answered by Penny Nom.
The volume of a truncated prism 2008-03-03
From jhey:
The volume of a truncated prism is 6240 cu cm. The base is a right section in the form of an equilateral triangle. The edges perpendicular to the base are 15 cm, 18 cm, and 15 cm long. Find the length of one side of the base.
Answered by Harley Weston.
Stanley Cup costume (truncated cone pattern) 2007-10-19
From Janet:
You hockey fans will love this question. I am making a Stanley Cup halloween costume and need a flat pattern for the bowl portion. I believe a truncated cone will work nicely. Base circumference needs to be 32" (10.19 diameter). Top circumference needs to be 44" (14 diameter). It needs to be 8" high. Thanks for your help.
Answered by Stephen La Rocque.
A truncated prism 2007-09-24
From Simon:
What is the name of a triangular prism with the top of the top of the prism cut off called please. It is therefore flat on top and flat on the bottom with prism sides. Thanks.
Answered by Harley Weston.
Solving an equation with fractions 2007-09-20
From Len:
I am having a brain cramp or maybe I just forgot some basic math, but I am having trouble solving for "r" in your truncated cone example where r/(r+w)=r/R or r/(r+282)=911/1728. Could you refresh my memory by showing the steps to solve for "r"?
Answered by Harley Weston.
A truncated cone 2007-08-24
From JUAN:
i need to create a template for a cone that has a 4 " opening at top, a 14" base and 12" tall.Can u tell me how to achieve this ?
u have similar problems but when i try to do it , is not coming up right , please help..

Answered by Harley Weston.
A truncated cone 2007-03-10
From Russell:
Hello, I have attempted to use two of your answers already given and had no real success. This young lady is making a cat food dispenser using a truncated cone. The top of the cone as a diameter of 5 inches with a height of 6 1/2 inches and diameter of 3 inches for the bottom.

Could you please map out a solution for the both of us to understand? Thank you so much for your time and for this wonderful service.


Answered by Penny Nom.
The volume of a styrofoam cup 2007-03-08
From leanna:
find the volume of a styrofoam cup if the diameter of the top is three inches, the diameter of the base is 2 inches, and the height is 4 inches.
Answered by Penny Nom.
A metal shroud for a outdoor fireplace 2007-03-06
From Arnold:
I am making a metal shroud for a outdoor fireplace, it is basically a lampshade type pattern,like the bottom of a cone.The top has to be 6 inches to fit the 6 inch stovepipe,and the bottom will be a 24 inch circle. the sides will be 18 inches in length.With the cost of the sheet metal,I can only afford to cut this out once,can you help me with the pattern ?
Answered by Penny Nom.
Motorcycle expansion chamber design 2006-11-14
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.
Constructing a cone 2006-09-20
From Suresh:
i want to know the required size of plate for cone rolling,sizes are 2950mm is bottom dia,894 is top dia and 600 is height.I have already read u r answers but i little bit confused ,harely and sue have given useful answers but when i worked both method the required plate size is different. so i like to know which method is easy and correct.and also i like know whether it can be rolled without segment my rolling machine width is 1500.
Answered by Penny Nom.
A truncated cone 2006-05-28
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.
The radius of a soccor ball 2006-05-05
From Jacqui:
A soccer ball is made up of hexagons and pentagons with the same side lengths. A manufacturer wants to produce a ball of certain diameter. The questions that follows is what side length for the polygons will produce a ball of certain diameter.
Answered by Chris Fisher.
How wide is this runway? 2006-04-27
From Sam:
A runway is 3.75 miles long and covers a total of 5.6 acres. What is the width of the runway?
Answered by Stephen La Rocque.
A lampshade shape 2006-02-11
From Rose:
Is there a solid shaped like a lampshade? Or do you just call it the bottom portion of a cone?
Answered by Penny Nom.
A pattern for a truncated cone 2005-12-04
From Nick:
I need to make a large cone segment. The large end has ID of 57 inches and the small end has ID of 23 inches. The cone is essentially a 45 degree cone (90 degrees at the tip). The sides of the segment are 2 feet long. How do I lay out a flat pattern that will fold into this segment? I need to know radius 1 and radius 2 and the angle the piece must be.
Answered by Penny Nom.
A truncated cone 2005-12-03
From Sonny:
I need to create a template for a cone that has a 2" opening at the top, a 4" base and stands 6" tall. Can you tell me how to achieve this?
Answered by Penny Nom.
A pyramid with its top cut off 2003-07-21
From David:
What is the name given to a 3D shape that looks like a pyramid with its top cut off?
Answered by Penny Nom.
Runs 2003-03-16
From Diana:
How many arrangements are there with n 0's and m 1's, with k runs of 0's? (A run is a consecutive set [1 or more] of the same digit; eg. 000 111 0 11 00 has three runs.)
Answered by Penny Nom.
The percentage grade of that hill 2002-11-05
From Cathy:
If there is an 80ft climb over a kilometer(about 3280ft) what is the percentage grade of that hill?
Answered by Penny Nom.
Running Through a Train Tunnel 2000-04-01
From Eugene Chan:
A man is running through a train tunnel. When he is 2/3 of the way through, he hears a train that is approaching the tunnel from behind him at a speed of 60 mph. Whether he runs ahead or back, he will reach an end of the tunnel at the same time the train reaches that end. At what rate, in miles per hour, is he running? (Assume he runs at a constant rate.)

I think the answer (12 mph) is wrong. Also, I believe it should read 1/3 of the way through, but don't know how to prove it. Could you come up with some way to prove it, please? I would really appreciate it.

Answered by Penny Nom.



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