







Volume of a spherical cap 
20190712 

From Shanto: In a jar of water, we kept a sphere with radius r. Then 75% of its volume went under water. Find out the distance of the top of the sphere from the surface of the water. Answered by Penny Nom. 





The surface area of a dome 
20181218 

From Chithrabhanu: If a dom dia is 4.552 and the height is 1.21 what is the surface area? Answered by Penny Nom. 





The code on a new phone 
20180202 

From Maria: Hi 
My husband gave me a new Samsung Galaxy mobile for out anniversaire gift. He set me a challenge which I have to solve before I can use the Phone. He has set the pin code with numbers 4, 7 and 0 and created a four digit code with the said numbers. Is there a way I can somehow list all possible combinations and try them all? Thanks! Answered by Penny Nom. 





A pool with a dome 
20170911 

From Bruce: A round 24 foot pool. A dome 3 feet above pool in center. How many feet across is the dome touching top rail straight across of pool? Answered by Penny Nom. 





A lock with 3 tumblers 
20170729 

From Carol: I have a lock that has 3 tumblers. The numbers are 0  9. I cannot recall what I set the combination to. How many combinations will there be with three numbers? Answered by Penny Nom. 





The area of a domed roof 
20151113 

From Brandon: I have a tank with a 13' radius that has a domed roof of 3.5' tall How do I figure out the area in SQFT? Answered by Penny Nom. 





The surface area of a circular dome 
20140410 

From Shafiqah: Is this a dome's surface area formula??
{{2 × π r × h square units}}
Is the surface area of the floor for the dome is calculate too in this formula?
Thanks for answering. =) Answered by Robert Dawson and Penny Nom. 





The surface area of a dome 
20120606 

From sravya: how to calculate surface area of a dome if its base radius and height are known and neither it is hemisphere nor radius of sphere is known?? Answered by Walter Whiteley. 





Two great circles 
20111006 

From Jean: "Two great circles lying in planes that are perpendicular to each
other are drawn on a wooden sphere of radius "a". Part of the sphere
is then shaved off in such a way that each cross section of the
remaining solid that is perpendicular to the common diameter of the
two great circles is a square whose vertices lie on these circles.
Find the volume of this solid."
I don't understand the geometry of the problem.
Can you please explain the problem and if possible draw a diagram for me
? Answered by Chris Fisher. 





Painting a hemispheric dome 
20100509 

From Jone: If a hemispheric dome has a height of 20m and it take 5 gallons of paint
to paint the floor, how many gallons of pain are needed to paint the
inside of the dome? Answered by Penny Nom. 





Surface area of a dome 
20090916 

From Charlie: Why is the calculation for the surface area of a domed tank less than the surface area of a flat top tank.
Using domed tank formula 2*pi*r(r(rdome ht) works out to be less surface area than a flat top tank area formula pi*r x r,
Shouldn't the dome have more surface area than the flat surface ? Answered by Harley Weston. 





A spherical dome 
20090803 

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. 





Two circles on a dome 
20090701 

From Beth: My question is related to a dome I would like to construct, for which I know the circumference of the base: 120ft.
I now need to figure out the diameters of two smaller circles, one at 20ft along the arc of the dome form the ground,
and the other at 30ft along the arc.
Assuming a true hemisphere, or 180 degrees total arc, how can I calculate these two circumferences?
Beth Answered by Stephen La Rocque. 





The surface area of a tank 
20090625 

From Charles: I need to calculate the external wall and top sqft surface area of a tank 54ft od x 15ft high with a dome top 54ft od x 8ft high. Answered by Penny Nom. 





Exterior square footage of a dome 
20080819 

From Richard: I have to gold leaf a dome with a circumference of 29'. What would the exterior square footage be? Answered by Penny Nom. 





The surface area of a dome 
20070211 

From chris: I need to figure the surface area of a dome which is 96" across and 48" tall. Could you help please? Thanks! Answered by Penny Nom and Melanie Tyrer. 





A dome with a square base 
20061017 

From Danielle: I need to know how to calculate the area of a dome that has a square base. In order to insulate the room I need to find the area of it but I am not sure how to do so because there is no formula for domes with square bases. Basically, the floor has 4 corners but the ceiling is dome shaped starting directly from the floor. Answered by Stephen La Rocque and Penny Nom. 





The Mitchell Park Domes 
20060401 

From Nicole: I would like to know how I could find the volume underneath the Mitchell Park Domes? The Diameter of the Domes is 140ft, 85ft high and 15,000 square feet. Answered by Stephen La Rocque. 

