







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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 

