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Water in a spherical container 2014-10-17
From Natalie:
A spherical container with radius 10cm being filled with water such that the water level, h cm, in the container increase at a rate of 0.5 cm s^(-1). Show that the area of the horizontal surface of water, A cm^(2), in the container is given by A = π(20h - h^(2) ).
Answered by Penny Nom.
Water in a hemispherical bowl 2012-05-12
From Jimmy:
A bowl of water, being a hemisphere has a radius of 36cm. Water is filled in the bowl and has depth of 18 cm. Find the surface area of the water?
Answered by Penny Nom.
Great circle course 2012-01-25
From Hervé:
On the earth, the mathematical formula giving the distance between two points, and the initial course for a boat on the great circle is well known. I need to find the inverse formula, ie knowing an initial position on earth, and the initial course of the boat, and the distance to run on the great circle, the formula gives the final position (longitude and latitude).
Answered by Robert Dawson.
A spherical ball in a conical wine glass 2011-10-26
From Jules:
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)).
Answered by Claude Tardif.
A triangle on a sphere 2009-09-07
From Rohit:
How do I find the angles of a triangle drawn on a sphere (spherical triangle)?
Answered by Chris Fisher.
A spherical dome 2009-08-03
From Eric:
I have recently been asked to resurface a dome sculpture for my local council but i'm having problems working out the area. Here are the dimensions. The height of the dome is 3m from the ground to the top of the arc. The arc itself from the ground rising up to the 3m point and back down, is 10m. The dome is 7m wide from one side to the other through the centre, at ground level.
I hope there is enough detail here. It's been a long time since i was in a maths class. Thank you, hope to here from you soon!

Answered by Stephen La Rocque.
A convex quadrilateral in spherical geometry 2008-07-09
From Joan:
What is the min and max number of obtuse angles possible ia a convex quadrilateral in Spherical Geometry? I know that the Saccheri has 2 obtuse angles and the Lambert has one, but are there other possibilities? Thanks for your help.
Answered by Chris Fisher.
A spherical bowl 2006-11-26
From Lynne:
A spherical bowl of internal radius 15cm is partly filled with liquid. If the radius of the horizontal liquid surface is 12cm, calculate (taking the value of pi to be 3.142), the height of this liquid surface above the center of the bowl.
Answered by Penny Nom.
The volume of water in a sphere shaped water tower 2006-05-14
From Dan:
I work in the water industry, providing automatic controls for water systems. I was wondering if there was a formula for calculating the volume of water in a sphere shaped water tower? With the use of a pressure gauge we know the elevation of zero water {the bottom of sphere) and the overflow elev. (near the top of sphere) I would like to calculate how many gallons are at any elevation in between.
Answered by Stephen La Rocque.
Non-euclidean geometry 2003-12-08
From Geoffrey:
How can you use non-euclidean geometry to navigate on a sphere? What geometers did work in this area?
Answered by Chris Fisher.
Non-Euclidean geometry 2003-12-03
From Geoffrey:
What are the applications of Non-Euclidean geometry (especially hyperbolic and spherical)?
Answered by Walter Whiteley.
Surface area of a contact lens 2000-06-06
From Evie Contreras:
I would like to know how to calculate the surface area of a contact lens with a radius of 7mm? I know that the area of a circle is pi R squared, but a contact lens has a dome.
Answered by Harley Weston.
Non-Euclidean Geometry 1999-02-10
From Robert Smith:
Is non-euclidean geometry necessary for the college bound student? I have students that are inerested in teaching math one day. My school is restricted to Euclidean Geometry.
Answered by Walter Whiteley and Jack LeSage.



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