







A cone formed from a circular sector 
20180418 

From Jessica: A circle has a radius of 7.5cm. A sector with an angle of 240 degrees is cut out from the sector. If the sector is folded to form a cone. Find the length of the cone. Answered by Penny Nom. 





An arched window 
20170724 

From Gerry: Looking to make a full size template for an arched window. Need increments every 16". The radius is 138' 0 9/16" , the chord is 226" and the rise at center of chord is 43" Answered by Penny Nom. 





The volume of a slab 
20170121 

From Russell: Working with a segment of a circle. The O.D. is 3.440" the length of the chord is 3.130 I need information on the volume of the largest area. I would like to know (in thousands of an inch) how tall would the largest area need to be to equal .1143 cubic inches If you need more info I can send it Thanks in advance Answered by p. 





Heights at various points along an arc 
20160415 

From Isiah: So I am working on a problem with a few friends; you have an arc with the center of its chord at 0,0. We also have a known sagitta and a known radius of curvature.
How do we calculate the height extending in both the positive and negative directions?
Central sag: 2.48
Chord length: 9.6 Answered by Penny Nom. 





Archimedes, Euclid and "Circular Reasoning" 
20151115 

From Ron: I have read about Archimedes and his work with sphere in cylinder and cone in cylinder and the volume relationships. Did he or any others also extend this to regular based polygon based regular like pillars, and columns? The ratio of 1/3 to 1 whole holds true with all regular based columns as example: a regular pyramid having a regular hexagon base inside a regular hexagon column of equal height. Answered by Chris Fisher. 





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. 





Reinforced steel mesh in a circular foundation 
20150822 

From Padmesh: in a circular foundation we are laying a reinforced steel mesh . i.e., like chords in both ways. the circle diameter is 2.91m and rods are placed 0.1m spacing. so I want to find the number of rods present in that circle. here by I am attaching an auto cad drawing for your reference Answered by Penny Nom. 





The surface area of a round bar 
20150606 

From chirag: Please tell me the formula for finding round bar surface in square inches/ mm Answered by Penny Nom. 





A parallelogram inscribed in a circle 
20150204 

From narendra: how can we prove that a circular parallelogram is a rectangle? Answered by Chris Fisher. 





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. 





Can a cylinder be considered a circular prism? 
20140208 

From Davina: Can a cylinder be considered a circular prism? Answered by Penny Nom. 





A square inscribed in a circle 
20131014 

From Jenn: Hello! I am about to buy a 7'9" round rug, but I want to have it cut down into a square. What's the largest square I can obtain from this? Thank you! Answered by Penny Nom. 





A semicircular roof gutter 
20120409 

From Kyle: A semicircular roof guttering contains some water.
The crosssection of the guttering has a diameter of 10 centimetres. The surface of the water collected in the guttering is 8cm.
What is the depth of water in the gutter? Answered by Penny Nom. 





A man made circular lake 
20101125 

From ailish: A man made circular lake has a diameter of 338 m. A bridge is to be constructed across the lake in such a way that it is 119 m away from the center of the lake. How long is the bridge? Answered by Penny Nom. 





May Lee's cake 
20100918 

From Wafa: May Lee bought a cake which is circular in shape. Her sister ate a quarter of the cake. Given that the area of the top surface of the remaining portion is 520 square cm, find the diameter of the cake. Answered by Penny Nom. 





Two cars on a circular track 
20100812 

From david: If two cars starts to drive at point 1 and go in a circle when will they meet?
(one cars speed is faster the other ) all I need is a formula Answered by Tyler Wood. 





A pile of sand 
20091216 

From Malik: Sand is leaking out of a hole at the bottom of a container at a rate of 90cm3/min. As it leaks out, it forms a pile in the shape of a right circular cone whose base is 30cm below the bottom of the container. The base radius is increasing at a rate of 6mm/min. If, at the instant that 600cm3 have leaked out, the radius is 12cm, find the amount of leakage when the pile touches the bottom of the container. Answered by Harley Weston. 





A circular border around a pool 
20090908 

From Calvin: A pool in the shape of a circle measures 10 feet across. One cubic yard of concrete is to be used to create a circular border of uniform width around the pool. If the border is to have a depth of 3 inches, how wide will the border be? ( 1 cubic yard=27 cubic feet ) Answered by Stephen La Rocque. 





4 couples seating themselves at a round table 
20090904 

From Hui: Q: 4 couples seating themselves at a round table. Men must seat together and women seat together. How many ways are there? Answer in the printed text is 576. I got 144. Pls advice. Answered by Claude Tardif. 





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. 





A semi circular room 
20090211 

From Taylor: being 450pi (the area of a semi circle)
how much money would it cost to lay carpet at $2.57 per foot???
if the area of a semi circular room is 450 pi ft
then what is the volume being that the diameter is 60 feet
and the ceiling is 16 feet tall Answered by Robert Dawson and Penny Nom. 





Seating around a circular table 
20090209 

From Jenny: A committee of 15  9 women and 6 men  is to be seated at a circular table (with 15 seats). In how many ways can the seats be assigned so that no two men are seated next to each other? Answered by Victoria West. 





Three circular rings 
20081218 

From seema: three circular rings of equal radii of 1cm each are touching each other.
a string runs all around the set of rings very tightly. what is the minimum length
of string required to bind all the three rings ? Answered by Robert Dawson. 





Jogging around a circular track 
20081119 

From kim: Joan wants to jog 10 miles on a circular track 1/4 miles in diameter. How many times must she circle the track? Answered by Penny Nom. 





The volume of fluid in a semi circular trough 
20081010 

From Kerry: How do I find the volume of fluid in a semi circular trough? Answered by Penny Nom. 





A bowl is the shape of a hemisphere 
20080428 

From josh: a bowl is the shape of a hemisphere with diameter 30 cm and water is poured into the bowl to a height h cm. how do i find the volume of the water in the bowl Answered by Harley Weston. 





The radius of a circular arc 
20080204 

From Bill: Hi,the Central Angle of a sector of a circle is 40 degrees. The circular arc of the curve has a chord length of 3000 ft. Find the radius(r) of the circular arc. Answered by Penny Nom. 





A large concrete shape 
20080116 

From Keith: what is the cubic yards of an area that is not a perfect 1/4 circle?
The dimensions are 100ft. x 60ft. x 125ft. curcumferal arch x 3ft. depth? Answered by Stephen La Rocque. 





An arched entry 
20071128 

From amber: i am working with an arched entry. i know that the radius is 25' and the height is 20'11". i need to know the length of the arch and degree of bend of the arch. how do i find these? Answered by Stephen La Rocque. 





A circular table is pushed into the corner 
20071031 

From Will: A circular table is pushed into the corner of a square room so that one point is 8 inches from one wall and 9 inches from the other. What is the radius of the table? Answered by Penny Nom. 





A cylindrical slab of concrete 
20070630 

From Kenn: I have a tank that needs a base of cement put in it. I dont know how to do this. The tank is 8 feet across and I want the cement to be 5 or 6 inches deep. Can you please tell me how much cement I need to do this. Answered by Harley Weston. 





Water tank volume 
20070529 

From Cecelia: I HAVE A SEMI CIRCULAR TANK AGAINST A WALL MEASURING 6'10" ACROSS THE WIDEST PART AND 3' FROM THE WALL TO THE FRONT OF THE TANK. THE DEPTH IS 14". PLEASE HELP ME TO CALCULATE THE VOLUME OF WATER IN THE TANK. Answered by Stephen La Rocque. 





Constructing an octagonal deck around a circular pool 
20070420 

From Cliff: [I am building an] octagonal desk encompassing 17 foot diameter circle for pool.
I have seen other octagonal calculations but none of these tell me how much allowance for a circle to fit within the octagon without losing the circle edge can anyone help
thanks cliff Answered by Stephen La Rocque. 





How many feet tall is the tunnel 
20061014 

From Charles: A tunnel in the Smoky Mountains is semicircular. At a distance of 12 feet from the center of the tunnel, the tunnel has a height of 16 feet. How many feet tall is the tunnel at its center? Answered by Penny Nom. 





Gallons of water in a well 
20060731 

From Martha: I have a shallow water well that is 30 feet in depth.
I have 8 feet of water in the well.
The water well is a 30 inch in diameter.
My question : How many gallons of water is in my tank? Answered by Penny Nom. 





A cone with vertex (1,1,2) 
20050926 

From Brandon: Find the equation of a double cone with vertex (1,1,2) and which intersects the xy plane in a circle of radius 4. Answered by Penny Nom. 





A seating arrangement 
20050203 

From Kay: If you have 5 married couples, how many arrangements can be made if they must sit across from each other? Answered by Penny Nom. 





A line from the center of the patch to the periphery 
20050101 

From Sandrine: I am currently researching a patch disease of grasses. These patches are roughly circular. I need a term for a line from the center of the patch to the periphery. Since the patches are not perfectly circular, my supervisors tell me I cannot use the word 'radius'. What else could I use? Answered by Denis Hanson and Harley Weston. 





Volume of a fuel tank 
20040301 

From Mike: I have a fuel ank for my big truck that has a radius of 24inches and a length of 65 inches. I am trying to compute the volume of fuel in the tank. I tried pie x the radius squared times the length but no usable results.
Can you help me please? Answered by Penny Nom. 





Volume of a tube 
20040114 

From Mike: where can you find how to get volume of a tube:
3 in across x 3 inch high
5 in across x 5 inch high
same formula for both. ONE will get the other. Answered by Penny Nom. 





Arrangements around a circular table 
20031007 

From Lori: How many arrangements can 6 people be seated round a circular table? Answered by Penny Nom. 





The volume of water in a hose 
20021113 

From David: I trying to find out how much water 500 ft of 3/4 inch hose will hold. I'd also like to know how you figured the answer. Answered by Penny Nom. 





A circular wading pool 
20020304 

From Patrick: The community of melfort is planning to build a circular wading pool in the park. The pool will cover an area of 1000m^{2}. The building committee has decided to put a 5m cement pad around it. How much additional area will the cement pad take up? Answered by Harley Weston. 





Building a circular silo 
20010124 

From Natasha: We wish to build a circular silo with internal diameter 10 feet. How much concrete will we need to pour the foundation, if we only need a 1 foot wide and 1 foot deep ring on which the silo walls will sit? Assume the 4 inch thick silo wall rests on the middle of the ring. Answered by Penny Nom. 





Circular Permutations 
20000918 

From J. Stuart: I am able to understand the simple theory behind circular permutations (that is, there are (n1)! ways to arrange n people in a circle. One question, however, is giving me some difficulty. It reads: In how many ways can four married couples be arranged around a circular table if each man must sit beside his wife? Any suggestions you have would be greatly appreaciated. Answered by Penny Nom. 





Trolls and Gargoyles 
19991102 

From TexGrimm: How can you seat 6 monsters  3 Trolls and 3 Gargoyles at a circular table if the trolls look alike and the gargoyles look alike? Does your formula work for 9 monsters  4 trolls and 5 gargoyles? Answered by Penny Nom. 





Circular Permutations 
19970205 

From Ed Varjassy: I have an understanding of simple problems involving circular permutations but do not understand them when they start to have restrictions. Is there any advice you can give for these more complicated permutations. Answered by Penny Nom. 

