







Why 1/2 in the area of a circular sector? 
20181026 

From Ariel: In the equation for area of a sector=1/2r^2theta why is it 1/2? Please explain conceptually not algebraically. Answered by Penny Nom. 





Form a cone from a circle sector 
20180812 

From Tinashe: A 216 sector of a circle of radius 5cm is bent to form a cone. Find the radius of the base of the cone and its vertical angle. Answered by Penny Nom. 





The perimeter of a sector of a circle 
20170811 

From Alisa: find the perimeter of the sector with radius 7 cm in which the angle at the centre is 60 degrees leave your answer in terms of pi Answered by Penny Nom. 





A sector of a circle 
20160421 

From mustafa: In a sector of a circle, the arc length is equal to half the perimeter of a sector.find the area of a sector in terms of r Answered by Penny Nom. 





Cutting a round cake so that it doesn't dry out 
20140826 

From James: I'm wondering if there's a simple way to calculate the area between two parallel chords of a circle equidistant from its diameter, or if I have the area, to find the distance between the two chords.
Here's my "problem". You may have heard of the way of cutting a round cake so that it doesn't dry out  make two parallel cuts (chords) the length of the cake, take the middle piece, then push the two pieces together.
So I know the area of a 12" cake, and I want say, exactly an eighth of the cake. How wide do I cut the centre piece?
Now to get even more difficult, the next day I want another eighth from the centre. How wide do I cut the next pieces, and so on...?
Thanks,
James Answered by Harley Weston. 





A circle is divided into three sectors 
20140417 

From atolagbe: the area of a circle is 154cm square. it is divided into three sectors such that two of the sectors are equal in size and the third sector is three times the size of the other two put together. calculate the perimeter of the third sector. take pi=22/7? Answered by Penny Nom. 





A triangular island 
20121229 

From Udit: A long time ago Mr Gibson found an island shaped as a triangle with three straight shores of length 3 km,4 km and 5 km. He declared an 'exclusion zone' around his island and forbade anyone to come within 1 km of his shore. What was the area of his exclusion zone? Answered by Penny Nom. 





Two sectors of a circle 
20120203 

From Wayne: I am not even sure what to ask. I have to two lengths of feet and an angle of degrees, and I have to find the area?
**Problem attached
Thanks,
Wayne Answered by Penny Nom. 





A sector of a circle 
20110107 

From Alice: the radius of a circle is 7cm the angle of the sector is 68 how do you find the Answered by Penny Nom. 





A sector of a circle 
20101129 

From Mel: Find the area of a sector of a circle that has a central angle of 13pi/18 and a radius of 12cm. Round answer to nearest 10th degree Answered by Penny Nom. 





The area of a field of view 
20100407 

From Frank: I know we have a field of view of 90 degrees and the distance we can cover is 6 miles. What is the area we can cover/view?
A formula would be nice to have since the diameter or distance of the wedge area can change and the degree of the field of view can also change.
Thank you and I look forward to hearing from you.
Frank Answered by Penny Nom. 





Water in a culvert 
20100318 

From Chip: Hello,
I have a problem to which I know there must be an analytical solution  but as it has been 50 years since I studied math I can't remember quite how to do it!! I have a 12" round culvert in my yard that runs water all year. I would like to be able to calculate the flow through the culvert by measuring the depth of water flowing through and measuring the speed of the current. I can measure the depth and the speed, but I forget how to calculate the cross section of the flow. If you could help I would greatly appreciate it.
Thank you Answered by Penny Nom. 





A sector of a circle 
20100204 

From trisha: Given a circle with a radius of 6 inches. Find the area of the sector that is formed by an arc of 36 degrees. Round your answer to the nearest tenth of an inch. Answered by Penny Nom. 





The area of a sector 
20100107 

From angelkem: how do you get the area of the circle, the sector, the shaded sector, non shaded sector and its total area if the diameter is 20 cm and each area of the circle is 45 degrees? Answered by Penny Nom. 





Annular sector 
20090720 

From Ed: What is the name for the section of a flat ring (annulus)? Similar to a section on a radar screen, a quadrilateral but the top and bottom are curved. Answered by Robert Dawson. 





The area of an arched transom 
20080928 

From Ivan: What is the formula for figuring out the square footage of arched transom windows & doors? Answered by Harley Weston. 





An exclusion zone around a triangle 
20080907 

From Awrongo: A long time ago Mr Gibson found an island shaped as a triangle with three straight shores of length 3 km,4 km and 5 km. He declared an 'exclusion zone' around his island and forbade anyone to come within 1 km of his shore. What was the area of his exclusion zone? Answered by Stephen La Rocque and Penny Nom. 





Arclength and sectorangle 
20080806 

From Benson: If chord length, radius are given, How to find the sector angle and arclength Answered by Janice Cotcher. 





The area of a sector of a circle 
20080510 

From lupio: a problem asks for the area of a sector in a circle,no central angle,in circle is given only 5cm radius, three answers 1809035
can't find a way to start.Help Answered by Harley Weston. 





The maximum area of a pizza slice 
20080412 

From charles: A slice of pizza in the form of a sector of a circle has a perimeter of 24 inches. what value for the radius of the pizza makes the slice largest[when o is the central angle in radians, the area of the sector is given by A= r^20/2and the length on the circle is given by s=r0 Answered by Harley Weston. 





The perimeter of a sector of a circle 
20080228 

From erica: What is the perimeter of a sector if the radius is 18 and the middle arc is 150? Answered by Penny Nom. 





A sector of a circle 
20080117 

From Amandsa: What is the formula for finding the sector of a circle? 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. 





The area of a sector of a circle 
20080111 

From Serenity: A denotes the area of a sector of a circle of radius r formed by the central angle theta.
Find the area A if r=10 meters and theta = 1/2 radians. Answered by Penny Nom. 





A portion of a circle 
20071207 

From Richard: please could you tell me the formula and answer to the following.
I have a circle portion with a radius of 150mm and an angle of 120 deg. If
an arc is drawn from one point to the other as the radii touch the circle
circumference, i need to know the area of the segment and the
formula to carry out the answer.
Many Thanks Answered by Penny Nom. 





Proving a quadrilateral is a rhombus 
20071203 

From Jeanie: How do you prove that a quadrilateral is a rhombus because the diagonals
of the quadrilateral are perpendicular and bisect each other using the 2column
proof method? Answered by Stephen La Rocque. 





Sides and vertices 
20071117 

From derek: What is the correct name for a 2D geometric shape that would look like one slice from a round pizza and how may sides and vertices would it have? I believe you would say it has one vertex and two sides with the curved boundary not resulting in vertices or a side. Your help is much appreciated. Answered by Chris Fisher and Walter Whitelty. 





The perimeter of a circle sector 
20071025 

From sara: Hi!
The area of a sector of a circle is 25 sqcm. The radius of the sector is 6 cm. Calculate the perimeter of the sector.
Many thanks!!! Answered by Penny Nom. 





Equation of a circle circumscribing a triangle with given vertices 
20071001 

From Randy: How do I determine the equation of a circle when it is circumscribed by a
triangle whose vertices are (1, 6), (3, 2), and (2, 5)? Answered by Stephen La Rocque. 





A sector of a circle 
20070926 

From A student: hi im stuck on this question. i have tried to do some, could you please che=
ck it and help me.the answers i have worked out are in red. the question is=
attached. thank you. Answered by Penny Nom. 





The area of part of a circle 
20070621 

From Sarah: Hi, I need help finding the area of a part of a circle that involves a
chord. I need this answer/help very soon if at all possible. I have
attached a drawing of what I am trying to solve. Thank you for your help!
Sarah! Answered by Penny Nom. 





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. 





Cutting the top off a circle 
20070225 

From Daniel: If a circle as a diameter of D I cut off a straight part at C from the top What is the formula to find the area of the left over part? Answered by Penny Nom. 





Sectors of a circle 
20061130 

From Maithreyi : A circle of diameter 21m is divided into three sectors with central angles 60degree,120degree and 180degree. Find the area of each sector? Answered by Stephen La Rocque. 





The area of a sector and a triangle 
20060623 

From Howard: I thought of the following problem which is similar but much simpler than the tethered goat problem: What is the angle(it is more illustrative in degrees)of arc of a unit circle so that the area between the chord it subtends and the arc length is equal to the area of the triangle with opposite side the subtended chord. Answered by Stephen La Rocque and Penny Nom. 





Overlapping area of two circles 
20060415 

From Jade: Given two identical circles where the radius (6 units) is the distance between the centers, what is the area of the overlapping region?
Answered by Stephen La Rocque. 





The square footage of an area in my backyard 
20060317 

From Kim: I need to find out how to calculate the square footage of an area in my backyard that is in the shape of a "slice of pie". There are two sides that are straight lines that come together at the top to form a point, and then at the bottom is a curved line that joins the two other lines together. I need to figure out how to calculate the square footage that is inside the area. Answered by Penny Nom. 





Sectors and arcs 
20060125 

From Wael: How is the area of an arc (alpha*pi*r squared/360) derived?
How is the length of an arc (alpha*pi*r/180) derived? Answered by Penny Nom. 





The area of a sector of a circle 
20060102 

From Natashia: How do you find the area of a shaded sector of a circle? Answered by Penny Nom. 





A 3dimensional pie shape 
20050917 

From Bill: Your site appeared in my search for the name of a 3dimensional pie shape. 2d would be a sector of a circle. As it it curved, I don't believe it is in a the polyhedra family. Can you help me find the mathematical term for it? Answered by Chris Fisher. 





Two overlapping circles 
20050320 

From Safi: I have a problem to calculate the area of two overlapping circles because two circles are overlap then how i calculate the overlap area to subtract from the area of both circle. Answered by Penny Nom. 





Irrigation and a sector of a circle 
20041223 

From Chuck: A friend of mine is a farmer and uses Pivots to irrigate portions of his land. The crop rows are in straight lines that all form chords of a large circle. The intent is to determine area between any two "boundary" rows expressed in acres. Answered by Harley Weston. 





The railing around a pool 
20040726 

From Bob: I have a 15' circular above ground pool. Around the perimeter of the pool are eleven (11) sections of railing. Each rail has 5 slots at each end for pins. I have calculated that the length of the arc under the railing to be 51.4". what I am trying to determine is the distance between the end points of the arc so that I can figure out which slot to use in the rails without going round and round the pool moving and removing the rails until they finally fit. Been there, done that, no fun. Answered by Penny Nom. 





Collinear Points 
20030113 

From Gary:
Which of the 4 points are collinear when you construct the following concurrent lines or rays of a triangle?  P(1), the point where the angle bisectors intersect.
 P(2), the point where the altitudes (or extensions) intersect (inside or outside of the triangle).
 P(3), the point where the medians intersect.
 P(4), the point where the perpendicular bisectors (or extensions) of the three sides of a triangle intersect.
This is for my 912 high school class in geometry. My name is Gary Thanks for your help. Gary
Answered by Harley Weston and Chris Fisher. 





Applied geometry 
20011102 

From Jenny: Where can I find some handson activities for my Applied Geometry classes? I want to do more activities with them that allow us to get out of the classroom. However, I want to use activities that use only inexpensive equipment because I usually buy the equipment myself. Answered by Walter Whiteley. 





Overlapping a circle and a square 
20001028 

From Jacky: A square with a dimension 20 by 20cm. and a quarter of the circle with the radius of 25cm (A quater of a circle is created by 2 cuts that are perpendicular bisectors of each other where the intersecting point is at the centre of the circle). With these 2 pieces, the 2 pieces are placed over each other in which the 90^{o} angle of the quarter circle matches with one of the right angles on the square. Now, calculate the overlapping area of the 2 figures. Answered by Chris Fisher and Harley Weston. 





Volume of oil in a tank 
19990417 

From Lars Waldemarsson: My problem is to get an equation for the depth of the oil in a gastank formed like a cylinder. The cylinder is in a horizontal position and by a stick you will be able to get the depth of the oil in the tank. All I need is an exmaple which I can build on. By this equation you will be able to get the volume of the oil if you know the depth. Answered by Harley Weston. 





Dig digs in the garden 
19990211 

From Katherine Shaw: A circular garden has an a radius of 8m. Dig, the dog, is tied up to a fence that runs round the outside of the garden. Dig was able to dig up all the garden, apart from an area of 64 square metres, which he couldn't reach. How long was his lead? Answered by Chris Fisher and Harley Weston. 





Concurrent Lines in a Triangle 
19980810 

From Chris Woolf: The question is Name four types of concurrent lines, rays, or segments that are associated with triangles. Answered by Chris Fisher. 





Area Between Two Sectors 
19970302 

From Rebecca Henry: Points A,B,C,D,E,F are equally spaced on a unit circle. Arc CGE has a center A. Find the number of square units of area in the shaded region. Answered by Walter Whiteley. 





Some Circle Questions. 
19970225 

From Staci Vawser: A circle with a radius of 10m is drawn. A chord is drawn across the circle. How is the area that is formed between the chord and the arc calculated? Answered by Harley Weston. 





Common Area of two sectors. 
19961106 

From Lynda Mow: How do I find the area common to two intersecting circles of radii 8 ft and 10 ft if their common chord is 10 ft long? Answered by Penny Nom. 

