A circle has a dia of 20 cms. What will the length of the arc over a chord of 5 cms lenth?
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To find arc length, you need the angle that the arc subtends and the radius of the circle.  To find the angle, you'd have to do some geometry...\n\nImagine a triangle with sides 10, 10, and 5.  This is pretty much a chord on your circle (5) and the radii from the center to the ends of the chord (10).  If you draw a line from the center perpendicular to the chord, it bisects the chord.  This gives you two right triangles, with hypotenuse 10, side 2.5 (half the chord), and side unknown (the segment from the center to the chord).  To find the angle at the center formed by the radius and the unknown, you can use the sine function:\n\nangle = arcsin(opposite/hypotenuse)\nangle = arcsin(2.5/10)\nangle = 14.48 degrees or 0.25 radians\n\nThe total angle is then 0.5 radians, since the above only found half of that total angle.\n\nThe formula for arc length is\n\narc length = radius * angle\n= 10 cm * 0.5 rad\n= 5 cm\n\nAnd this kinda makes sense - if the total circumference is 20pi, and the arc is 28.96 degrees, then the arc length can also be found by\n\narc length = angle * circumference/360\n= 28.96 * 20pi/360\n= 5 cm
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I'm not sure how far I'll get with this one, but I'll give it a try.\n\nLet the center of the circle be at (p,0), so the equation of the circle is (x-p)^2 + y^2 = a^2, with a>p.  The chord is y = mx, and we want to find where the chord and circle intersect.\n\n(x-p)^2 + m^2 x^2 = a^2\nx^2 - 2px + p^2 + m^2 x^2 = a^2\n(m^2 + 1) x^2 - 2px = a^2 - p^2\n\nSolve by completing the square (details omitted) to get\n\nx = {p +/- sqrt[m^2 (a^2 - p^2) + a^2]} / (m^2 + 1)\n\nThe center of the chord (hence center of the circle with chord as diameter) is at x = p / (m^2 + 1), with y = mx = mp / (m^2 + 1).  The radius is sqrt[m^2 (a^2 - p^2) + a^2] / (m^2 + 1), so the equation of that circle is\n\n[x - p / (m^2 + 1)]^2 + [y - mp / (m^2 + 1)]^2\n  = [m^2 (a^2 - p^2) + a^2] / (m^2 + 1)^2\n\nIf q = m^2 + 1, then by clearing fractions, we get\n\n(qx - p)^2 + (qy - mp)^2 = m^2 (a^2 - p^2) + a^2\n\nI'm not going to check my work, but those are the answers I ended up with.
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100 cm, its a 3:4:5 right triangle.\n\n[lay the cylinder out flat, if you will.  4 times around is 80 cm, and the width is 60 cm.  So the string has to form the hypotenuse of the 60 cm by 80 cm sided triangle.  60 divided by 20 is 3, 80 divided by 20 is 4, and a right triangle is famously 3:4:5, so 5 times 20 is 100 cm]
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For a simple wheel, you would use the formula.. \n\n(sin2 x)^2+(cos x)^2 =1\n\nsimilarly, every arc or every line drawn is formed of lines whose distance depends on the adjacent line or your screen size. (/2 or /4or some ration of it for position)
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Formula:arc length = radius * angle inscribed by arc, \n\nor:\n\nS=r*theta\n\nIf you know the arc length already, take a protractor and measure the distance in degrees between the two end points.\nConvert angle to radians by multiplying by pi/180, and then plug it into the equation and solve for r.
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I want to point out first that the formula for perimeter of a circle is (pi)d or 2(pi)r, not (pi)r^2- (pi)r^2 is for the area!\n\nAnyway, P= (pi)d\n         = 8pi\nDivide that by two since it's just a half circle\n         =4pi\nAdd 8 to that, and there you have it, the perimeter!\n\nFinal Answer- 4pi+8 or 20.56cm^2
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You can't. It depends on which way the diameter is turned in the circle. There are an infinite amount of solutions. Tell your teacher to be more specific.\n\ntosmith
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The area of segment of a circle is given by\nA = r^2[theta - sin(theta)]/2\n\ntheta is given by\ntheta = 2 arcsin(c/[2r])\n\nwhere c is the chord length and r is the radius.  So,\ntheta = 2 arcsin(c/[2r])\n= 2 arcsin(20/[2(12)])\n= 1.97 radians\n\nSo the area then is\nA = r^2[theta - sin(theta)]/2\n= (12)^2[1.97 - sin(1.97)]/2\n= 75.5 m^2\n\nEDIT:  My answer is indeed correct.  greatindiangenius's angle below is wrong.  You can find that angle theta another way besides the way listed on the link below - if you imagine a triangle formed by the chord and two radii, and if you drop a height from the center to the chord, then you have two triangles with long leg 10 and hypotenuse 12.  The angle between the height and the radius is arcsin(10/12) = 56.44, so the entire angle is 112.88 degrees, or 1.97 radians, not 100.\n\nRecall that a _sector_ is the pie wedge shape of a circle, starting from the center.  But a _segment_ is only the part between the chord and the circle - the ice cream part of the cone, if you break the _sector_ down like that.  So the formula in my reference and my work is correct in that we are finding the area of the ice cream only, and not the ice cream and cone.\n\nWe can find the area of the segment another way: we can take the area of the sector and subtract the are of the triangle formed by the radii and chord.\n\nFor the area of the _sector_, recall that it's just a fraction of the entire area, based on that angle 112.88:\n\nArea of sector = (112.88/360)(pi*12^2)\n= 141.85 m^2\n\nFor the area of the triangle, we need the height (we already have the base, 20).  We can use the Pythagorean theorem:\n\nc^2 = a^2 + b^2\n12^2 = 10^2 + b^2\n144 = 100 + b^2\nb^2 = 44\nb = 2sqrt(11)\n~ 6.63 m\n\nArea of triangle = (1/2)bh\n= (1/2)(20)(6.63)\n= 66.3 m^2\n\nArea of segment = Area of sector - Area of triangle\n= 141.85 - 66.3\n= 75.5 m^2\n\nwhich is the same thing as above with the other formula.
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H\n\nArea of first circle = pi*20^2 = 400*pi\nArea of second circle = pi*10^2 = 100*pi\npi(400-100) = 300*pi = 942
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Arc=r.theta=8*pi/8=pi
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the longest chord .... the one that passes through the center ... is a diameter
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0.5 (x) arctan(x) - 0.25 log (x^2+1)
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x = a*sin(ang)\ny = b*cos(ang)\n\nang goes from 0 to 360 degress, a and b determine how oval it is (if a=b it is a circle)
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Angle 2*pi is one revolution, so this arc is the circumference!\n2*pi*radius = 18*pi\n\nThere is also the general formula \narc length = radius * angle (in radians), which of course gives exactly the same result here.  But after 2 hours I guess you're not there to see this answer!  Sorry no-one responded earlier.
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The longest chord is 16, the short one is 12.\n\nFirst, for those of you playing along at home, here is the picture.\n\nDraw the large circle (radius 10) centered at (0,0), the small circle (radius 3.5) centered at (12.5,0). Draw chord in the large circle at (6,0), the chord in the small circle at (10,0). These are both vertical lines.\n\nLook at the large circle first. Half of the cord is one leg of a triangle with a hypontenuse of 10 (radius of the circle and a leg of 6 (10 - 4 overlap). This is a 6, 8, 10 (3,4,5) right triangle, so half the length of the chord is 8, its length is 16.\n\nNow look at the small circle. Half of the cord is one leg of a triangle with a hypontenuse of 6.5 and one leg of 2.5,\nthis is half of a 5,12,13 right triangle so the other leg is 6, the length of the chord is 12.
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You should be doing your own homework.\n\nYou need to know the diameter of Jupiter in meters.\nConvert that number of meters to AU.\nUse the definition of "sin" (or "tan").\nOne second of arc is 1/3600 of a degree.
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---------Y cm----------\n==========\n    1 cm\n_______________________\n          "           "   '\n    1.5cm "    B      "   '\n         _"__x cm_____"   ' \n  A       "           "   '3.5 cm\n      2cm "           "   ' \n__________"___________"   '\n\n\n7/2= 3.5\n\n3.5 cm- 2 cm= 1.5 cm\n\nY cm- X cm = 1 cm (from statement "The length in the hole is 1 centimeter less than the length of metal sheet. Length of metal sheet is Y cm, therefore, Y cm- 1 cm= X cm or Y cm - X cm= 1 cm).\n\nIf you compute the area of Rectangle A, that would be..\n\nlength x width = 3.5 cm x 1 cm = 3.5 cm sq.\n\n"After the whole is cut, are of remaining metal is 11 cm squared"... therefore\n\nArea of Rectangle A + Area of Rectangle B = 11 cmsq.\n\n11 cm sq. - 3.5 cm sq= 7.5 cm sq.\n\n\nGiven: Area of Rectangle B is 7.5 cm sq.\n       Length x width  (rect. B) = 7.5 cm sq.\n\nWe know width is 1.5 cm (from 3.5 cm- 2 cm).\n\nSolve: Length x width = Area\n       Length x 1.5 = 7.5\n       Length = 7.5 / 1.5\n       Length = 5\n\nTherefore:\n\nLength of x (hole) = 5 cm.\nLength of Y (metal sheet) = 5 cm + 1 cm. = 6 cm.\n\nI hope this helps. Let me know if you have other questions.