







A stained glass cone lamp 
20160409 

Edwin pose la question : In making a 16" dia. cone lamp (stained glass), how many square feet of glass do I need. Penny Nom lui répond. 





Water in a conical funnel 
20140211 

Marcus pose la question : Water is running out of a conical funnel at the rate of 1 inch^3/sec. If the radius of the base of the funnel is 4 in. and the altitude is 8 in., find the rate at which the water level is dropping when it is 2 in. from the top. Penny Nom lui répond. 





Conics 
20140201 

Kassidy pose la question : Hey, I have searched through all the questions about conics and how
people use them in the real world, but none of them were very specific
on how they are applied and the process, why it's so important etc.
I have a project due asking these questions and it's been very difficult
finding the right answer, if you could name jobs, how they are use and
specifically applied that would be greatly appreciated. Penny Nom lui répond. 





Related rates 
20140130 

Veronica pose la question : A container is the shape of an inverted right circular cone has a radius of 1.00 inches at the top and a height of 5.00 inches. At the instant when the water in the container is 1.00 inches deep, the surface level is falling at the rate of 2.00 inches/second. Find the rate at which the water is being drained. Penny Nom lui répond. 





conical lamp stand/staved wood 
20131207 

Henry pose la question : need to make lamp stand that is wooden staved; need it to be 25 inches at bottom and 10 inches at top; need to know angles for staves to be cut; the lamp stand will be rounded on a lathe and will be 40 inches tall John Lucas built one and it is pictured on his web page. thank you for any help/direction; I checked out the answered for cone shaped objects on your page but didn't find what I could use. thanks again. Henrywoodturner, parent teacher student . . . . . Harley Weston lui répond. 





Three piles of top soil 
20121007 

Steve pose la question : I need your help please, I am looking to purchase some top soil and keep getting conflicting answers.
There are 3 piles and here are the sizes;
Pile #1: 203 feet around and 21.29 feet high.
Pile #2: 195 feet around and 18.75 feet high.
Pile #3: 150 feet around and 17.98 feet high.
I look forward to hearing back from you asap.
Thank You!
Steve Harley Weston lui répond. 





The dimensions of a conical tent 
20120304 

yash pose la question : a conical tent is to accommodate 11 people.Each person must have 4m square of space on the ground and 20m cube at air to breathe.Find the height and radius of the conical tent.26202 Penny Nom lui répond. 





Water pouring into a conical tank 
20111121 

Patience pose la question : Hi my name is patience and I'm having a problem with this question.
Water pours into a conical tank of semi vertical angle 30 degrees at the rate of 4 cm^3/s, where h is the depth of the water at time t. At what rate is the water rising in the tank when h = 10 cm?
Thank you Penny Nom lui répond. 





A spherical ball in a conical wine glass 
20111026 

Jules pose la question : A heavy spherical ball is lowered carefully into a full conical wine
glass whose depth is h and whose generating angle (between the axis
and a generator) is w. Show that the greatest overflow occurs when the
radius of the ball is (h*sin(w))/(sin(w)+cos(2w)). Claude Tardif lui répond. 





A reservoir has the shape of an inverted cone 
20111003 

Roger pose la question : a reservoir has the shape of an inverted cone whose cross section is an equilateral triangle. if water is being pumped out of the reservoir at a rate of 2m^3/sec, at what rate is the depth of the water changing when the depth is 40 meters? Penny Nom lui répond. 





A conical container and a spherical balloon 
20110406 

Steven pose la question : Water is running out of a conical container 12 feet in diameter and 8 feet deep (vertex down) and filling a spherical balloon.
At the instant the depth of the water in the cone is 4 feet, the radius of the sphere is approximately 4 feet.
The rate of change of the depth of the water in the cone at the instant is approximately ______________ times the rate of change of the radius of the balloon. Penny Nom lui répond. 





At what rate is the grain pouring from the chute? 
20110226 

MJ pose la question : Suppose that grain pouring from a chute forms a conical heap in such a way that the height is always 2/3 the radius of the base. At the moment when the conical heap is 3 m high, its height is rising at the rate of 1/2 m/min. At what rate (in m^3/min) is the grain pouring from the chute? Penny Nom lui répond. 





Cutting the top off a conical tent 
20110222 

tom pose la question : how far from the top must you cut a conical tent in order to cut the
cloth in half... Penny Nom lui répond. 





Two conical tanks 
20110217 

rustom pose la question : Two vertical conical tanks (both inverted) have their vertices connected by a short horizontal pipe.
One tank, initially full of water, has an altitude of 6 ft. and a diameter of base 7 ft.
The other tank, initially empty, has an altitude of 9 ft., and a diameter of base 8 ft.
If the water is allowed to flow through the connecting pipe, find the level to which
the water will ultimately rise in the empty tank (Neglect the water in the pipe.) Penny Nom lui répond. 





Calibrating a conical tank 
20110205 

Bill pose la question : 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 Stephen La Rocque and Penny Nom lui répond. 





A conical pile of gravel 
20100515 

Chuck pose la question : If I have a conical pile of gravel 50 feet across at the base and a height of 65 feet and
the slope of the side is approximately 60 degrees, how do I calculate the cubic yards? Robert Dawson lui répond. 





A conical pile of gravel 
20100413 

Chassity pose la question : The gravel pile is 120' around at the base and goes up 20' high at the peak. How many tons or yards of gravel in that pile? Penny Nom lui répond. 





What jobs use conics? 
20091022 

denise pose la question : i have to type a paper on what jobs use conics and i can not find anything can you help
thanks
Denise Penny Nom lui répond. 





What type of conic section is this? 
20090522 

Donna pose la question : What type of conic section is 3x² + 3y²  4y  8 = 0 Penny Nom lui répond. 





The volume of water in a cone 
20090317 

Freddie pose la question : A ball of diameter 20cm rests in a conical container whose angle with the slant height and the vertical axis is 25degrees. if water is poured into the container just enough to touch the bottom of the ball, find the quantity of water in the container. Penny Nom lui répond. 





Water drains from a conical tank 
20090311 

Tyler pose la question : Water drains from a conical tank at the rate of 5ft/min^3. If the initial radius of the tank is 4' and the initial height is 10'.
a) What is the relation between the variables h and r? (height and radius)
b) How fast is the water level dropping when h=6'?
Thanks for the help, i'm stumped. Penny Nom lui répond. 





A conical sleeve 
20090217 

Jonathan pose la question : I'm having a hard time making a design pattern for a cone sleeve, the thing is the cone sleeve is 22 degrees, how can i know the angle of this when it is flat on paper, based on my calculations, it should be around 66  69, but i want it to be exact can anybody help? Penny Nom lui répond. 





Conics 
20090205 

Jay pose la question : If you were to design your own picture of a conic, what would it look like? And also if you had to use two conics from the solar system and a solar oven...? Robert Dawson lui répond. 





A conical funnel 
20081112 

Rachael pose la question : Hello, I am a 10th grader in AP Calc, and can not figure out this question:
Water is running out of a conical funnel at the rate of 1 inch^3/sec. If the radius of the base of the funnel is 4 in. and the altitude is 8 in., find the rate at which the water level is dropping when it is 2 in. from the top. Harley Weston lui répond. 





CIRCLES 
20080707 

daryl pose la question : Find the equation of the smaller circle that is tangent to the axes and the circle x(squared)+y(squared)=2x+2y1? Penny lui répond. 





Liquid is being pored into the top of a funnel 
20080525 

Stella pose la question : Liquid is being pored into the top of a funnel at a steady rate of 200cm^3/s. The funnel is in the shape of an inverted right circular cone with a radius equal to its height. It has a small hole in the bottom where the liquid is flowing out at a rate of 20cm^3/s. How fast is the height of the liquid changing when the liquid in the funnel is 15cm deep?
At the instance when the height of the liquid is 25cm, the funnel becomes clogged at the bottom and no mo re liquid flows out. How fast does the height of the liquid change just after this occurs? Stephen La Rocque lui répond. 





Conic sections 
20080414 

Christine pose la question : In my analysis class we are learning about conic sections.
Our project is to create a genral statement of the definition of conic sections.
Truthfully, I have absolutely no clue on how I should write that.
Could you help me? Walter Whiteley lui répond. 





Water in a conical tank 
20070910 

Greg pose la question : Joe is conducting an experiment to study the rate of flow of water from a conical tank.
The dimensions of the conical tank are:
Radius at the initial water level = 13.7 cm
Radius at the reference point = 12.8 cm
Initially the tank is full of water. There is a circular orifice at the bottom of the conical
tank with a diameter of 0.635 cm. The water drains from the conical tank into an empty
cylindrical tank lying on its side with a radius of 0.500 ft and a length L (ft).
Joe observed the water discharged with an average velocity of 1.50 m/s as the water level
lowered from the initial height of 14.0 cm to 5.00 cm in the conical tank. Answer the
following:
1. If the initial height of water in the conical tank is 14.0 cm (measured from the
reference point, see Fig. 1), how long in seconds will it take for the water level to drain to
a height of 5.00 cm?? NOTE: Height refers to the vertical height.
What formula would I use to find out how long in seconds it takes for the water level to drop? Harley Weston lui répond. 





Identifying a conic from its equation 
20070819 

Robin pose la question : Hi,
Do you have any tips how to identify a conic from its equation? Leeanne Boehm and Steve La Rocque lui répond. 





Parabolas in the real world 
20070518 

Katherine pose la question : Hi, my name is Katherine, and my mean old math teacher just assigned us a test in which
we have to write two examples of how parabolas are used in the real world, each one page
single spaced, size 12!! I know you have already answered some questions like this, but
I still don't understand the whole baseball thing, and any other way parabolas are used.
And how I can write a whole page on it. But that's my problem, not yours, I just need help
with a little explanation on how parabolas are actually used today. I know this might be kind
of confusing for you, but imagine how it is for me!! Stephen La Rocque lui répond. 





Maximizing the volume of a cone given the slant length 
20070514 

Christina pose la question : A coffee filter for a new coffee maker is to be designed using a conical filter. The filter is to be made from a circle of radius 10cm with a sector cut from it such that the volume of coffee held in the filter is maximised. Determine the dimensions of the filter such that the volume is maximised. Stephen La Rocque and Kerstin Voigt lui répond. 





A fountain as a parabola 
20070308 

Emily pose la question : I have to do a math project proving that something in real life is a parabola. I really need some help here because i don't know where to start. I want to do it on a fountain and prove it's a parabola but how do i do that? I would really appreciate it if you could help Emily Stephen La Rocque lui répond. 





What jobs involve using conics? 
20070221 

Nicki pose la question : What jobs involve using conics? Penny Nom lui répond. 





Things that are shaped like a parabola 
20070214 

carra pose la question : i can't find other examples of things that are shaped like a parabola except for bridges.............. Pls. help it is due tomorrow. thank you very much:) Steve La Rocque, Penny Nom and Walter Whiteley lui répond. 





Conic sections 
20061119 

Joyce pose la question : My son has a project on conic sections. I need the following information on Parabola, Circle, ellipse,and hyperbola. He can't find the following information for each conic section: equations with explanations, four uses for each shape and Shape explanation. Penny Nom lui répond. 





Wheat is poured on a conical pile 
20061117 

Rachel pose la question : wheat is poured through a chute at the rate of 10 cubic feet per minute and falls in a conical pile whose bottom radius is always half the altitude. how fast will the circumference of the base be increasing when the pile is 8 feet high? Penny Nom lui répond. 





Some applications of conic sections 
20061113 

Burt pose la question : how are circles, ellipses, and hyperbolas used in everyday life Penny Nom lui répond. 





The focus of a parabola 
20061001 

Lily pose la question : I have a mathematical assignment which includes applications of parabolas, hyperbolas and ellipses in the real world. I have been searching the internet and now I am ware that most of the applications of parabolas have a connection with what people call "the focus". However, I do not think I clearly understand what "the focus" of a parabola is. Would you please explain it to me? Penny Nom lui répond. 





A question on conics 
20060109 

Reb pose la question : i know how to convert the general formula into specific ones(ie.; a circle's specific formula x^{2} + y^{2} = r^{2} can be derived from this, and then you draw you graph), but i have no idea how to go from a graph to the general formula (you know the HUUUGE one...) Penny Nom lui répond. 





A conical hat 
20051022 

Manish pose la question : I need to make a conical hat for my daughter's upcoming fancy dress, the circumference of the base(hollow) is 50 cms,the height of the cone is 30 cms,what should be the dimensions of the paper which will make a cone of the beforementioned dimensions? Penny Nom lui répond. 





Quadratics 
20050105 

Usman pose la question : Hi, in my Grade 11 Functions math class we have been assigned the task of finding jobs and careers related to quadratics, I have done many searches but have been unsuccessful, then I saw your website and emailed. I also have to use an example of a math problem that the job uses, then solve it, this will all compile on bristol board for a presentation. I would greatly appreciate it if you could send me some links and references of sources that refer to this subject. Harley Weston lui répond. 





An elliptical table 
20050103 

Roger pose la question : Want to make an elliptical table, say the long (major) axis is 4 feet, and the short (minor) axis is 3 feet. I can construct this figure, but I'm trying to figure out what the exact dimension of a rectangle within this ellipse will be if I make the table a drop leaf type where the drop dimensions are equal for each end of both the long and short axes. Intuitively, it looks like there is one and only one solution. Penny Nom lui répond. 





Practical applications: parabolas and Pythagoras 
20041024 

Connie pose la question : Provide two examples of real life objects that incorporate parabolic shapes. Explain the reason why the parabolic shape was used in each object.
I need at least one practical application of the Pythagorean Theorem. Penny Nom lui répond. 





A conic 
20040810 

A student pose la question : My question is about this equation 32x*2 18y*2 64x +72y +248 =0
explain why as x goes to the infinity the graph of the conic looks like y= (3/4)X.
What I did to try to find the solution of this problem was to graph and then I thought that maybe trying to find the equation of the asymptotes I could do it, but it was useless because the equation of the asymptotes is y= +4/3(X1) 2 and that does not explain why tho conic looks like y=(3/4) x . I would really appreciate your help on this. Penny Nom lui répond. 





Uses of conic sections 
20030401 

William pose la question : My name is William and I am doing a research paper on conic sections for my 12th grade math class. Part of the project is to find two conic sections in our world today and explain what there purpose is. I really need help in this area because I've been searching the internet for where conic sections are used in our world today and I really can't find anything. If you can tell me specific building or a pyramid that contains conic sections that would be great. Or even something in the universe would be helpful. Leeanne Boehm lui répond. 





The intersection of conics 
20021219 

Glenda pose la question : We are studying systems of equations where two conic sections are the two equations that we are solving simultaneously. We were studying the number of solutions that are possible if you have an ellipse and a parabola. We all agree that there can be none, one, two, three or four solutions. The question that the students had for me was whether or not a portion of an ellipse and a parabola can overlap and thereby allow an infinite number of solutions. What should I tell them? Chris Fisher and Harley Weston lui répond. 





A lampshade from a cone 
20021126 

Ellsie pose la question : I need to make a pattern to cover an old lampshade. This is actually the bottom portion of a cone. Please help me figure out how to draw this pattern, so that we can complete our project. Penny Nom lui répond. 





A paper model of a cone 
20020814 

Bruce pose la question : I have made a paper model of a cone, cut a sloping section, and removed the top. I have drawn the major and minor axis on the paper surface of the section. The major axis is not symmetrical about the minor axis. To me, this is not an ellipse. To me, an ellipse is a tubular section, because this gives a symmetrical major axis. What is your opinion? Walter Whiteley and Chris Fisher lui répond. 





Conics 
20020529 

Brooke pose la question : Which conic cannot be generated by an intersection of a plane and a double napped cone? Chris Fisher lui répond. 





Parabolas 
20020203 

Kuang pose la question : Who is credited for working with or studying the Parabola? What is a conic section? What does a parabola look like? How is a parabola formed? Where and how are parabolas used today in the real world? Harley Weston lui répond. 





Water in a conical tank 
20011020 

Sarah pose la question : The problem: Water flows into a conical funnel at a continuous rate of one gallon per minute (One gallon = 231 Cu.In.). The height of the funnel is 5" and the diameter is 8". The 1st formula: I need to develop a formula that will give the volume, in cubic inches, of the water in the funnel at any time t (in seconds). V = f(t). The 2nd formula: I need to develop a formula that will give the height of the water in the funnel at any time t (in seconds). h = f(t). Penny Nom lui répond. 





Quadratics 
20010516 

John pose la question : I am in the final stages of a math project and I need to interview an expert for the last part. Please try to answer at least a few of these questions.  How do you use quadratic equations in your everyday life?
 Do you find being a math expert very helpful in life?
 Is the quadratic equation useful to you?
 Why did you decide to become a math expert?
 What do you think is the most important function of the quadratic equation?
Harley Weston lui répond. 





A pile of sand 
20010514 

Gul pose la question :
 Sand for use on icy roads is stored in a conical pile 14.2 m high and with a base diameter of 34.4 m
 calculate the volume of the pile
 if one sander can take 6.9 m of sand, how many sanders can be filled from the pile?
Penny Nom lui répond. 





Circles, ellipses, parabolas and hyperbolas 
20010509 

Colleen pose la question : How is an ellipse like a circle? In what way does an ellipse have a center? How is a hyperbola similar and different to an ellipse? How is a parabola similar a different to a circle ellipse and parabola? Pnny Nom lui répond. 





Bridges and parabolas 
20001118 

Lauren pose la question : My name is Lauren, and Im a secondary school student in Ontario. For my gr11 advanced math class I have to find out how and why parabolics are used in arch bridges and write 3 paragraphs on it. People who cohse satelites and whatnot are lucky  I've found a ton of info, but for arch bridges there seems to be nothing. Harley Weston lui répond. 





A conic in standard form 
20000518 

Tara McConkey pose la question : Im havign trouble converting the following conic to standard form, i know that the conic is a hyperbola but that is all 16x^{2}9y^{2}160x18y+247=0 Harley Weston lui répond. 





Rectangular hyperbola 
19991215 

Aarti Chand pose la question : Why do they call a rectangular hyperbola, rectangular and where the normal hyperbola looks like a rectangle and the rectangular hyperbola looks like a sqaure? Chris Fisher lui répond. 





Two conics 
19991207 

Quinn pose la question : I know the formula to find the axis of symmetry of a conic section (I'm not sure what shape  circle for the first one??) is (D/2A,E/2C) but I obviously don't get how to calculate it, because when I check the answer it's wrong, but I'm so close!! For the following equations my teacher suggested to "divide the x term coefficient, D, by the x squared term coefficient before...do the same for y." 2x^{2}+2y^{2}8x+12y+16=0 . . . Penny Nom lui répond. 





Graphing Inequalities of Conic Sections 
19970324 

James Sheldon pose la question : I'm trying to graph Systems of Conic Sections with inequalities, but I'm running into problems on which area to shade: x^2+y^2 is greater than or equal to 16 xy > 4 So I graph these two equations, and then my teacher said to substitute a point into it but I'm still not sure how to do it... Penny Nom lui répond. 

