how can calculate the radious of a circle by just having an arc of it?
488009
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.
747001
I'm assuming you are familiar with calculus.  Consider an infinitesimal cylinder at height 'y' of thickness 'dy'.  The surface area of that cylinder is 2*pi*Radius*thickness.  Here the radius is simply 3e^2y, and 'dA' the infinitesimal area is given by 2*pi*3e^2y*dy.  To get the total area gotten by rotating this curve, (note we don't have to do any rotation as its already factored in by the assuming an infinitesimal cylinder) simply integrate between 0-3 the above expression, which I leave as an excercise for you.  Hope this helps.
141519
It is the length divided by the radius
407600
The area of the segment is given by\n\nA = r^2[theta - sin(theta)]/2\n\nSo we need theta, which is the angle that contains the chord, and the radius of the circle.\n\nThe radius of the circle is given by\n\nr = (c^2 + 4h^2)/(8h)\n= (20^2 + 4(6)^2)/(8*6)\n= (400 + 144)/48\n= 11.3 m\n\ntheta is given by\n\ntheta = 2 arcsin(c/[2r])\n= 2 arcsin(20/[2(11.3)])\n= 2.17 radians\n\nSo\n\nA = r^2[theta - sin(theta)]/2\n= (11.3)^2[2.17 - sin(2.17)]/2\n= 85.92 m^2
859740
This is not a rigorous way to do it, but it works all the same:\nYou know that 4=y^2+x^2 is the equation for a circle of radius 2 centered at the origin.  The line y=0 is just the x-axis.  So find the area of the top half:  A = ½πr² = ½π(4) = 2π\n\n*If you had actualy integrated it, it would have been ugly:\nint[√(4 - x²)*dx] from x=-2 to x=+2.
237156
Pi * r^2\n\n(Pi R Squared)\n\nwhere R is the radius (which is also equivalent to half the diameter)
1174230
I think you have to know how many degrees the segment is.  Then, calculate the area of the entire circle:\n\nPI x radius ^ 2 (squared)\n\nThen, divide the degrees in the segment by 360, so if your segment is 54 degrees, it's:\n\n54/360 = .15\n\nThen, multiply the result of the 2nd calculation (.15 in the example) by the area of the circle you calculated in step 1, and there's your answer.\n\nThere's probably a more elegant way, but it's been 25 years since I took a trigonometry or algebra course.
351138
You got it.\n\nThe equation of a circle in standard cartesian from is:\n\n(x-a)^2+(y-b)^2=r^2\n\nThe circle is centered at (a,b) and r is the radius. For you, (a,b) is (0,0) and your r^2 term is 49, hence your r is the square root of 49 which is 7.
966696
Arc=r.theta=8*pi/8=pi
830100
'x= rcost\ny=rsint\n\nand r= sqrt(x^2+y^2)\nt=arctan(y/x)\nso\nif x=2, and y=2, then r= sqrqt(4+4)=sqrt(8)\nand t=arctan(2/2) = arctan(1) = pi/4
549743
Area increases 4 times. Beacause Area of circle = PiR2.\n\nSo if R doubles then radius will be 2R.\n\nHence area will be Pi(2R)2. which results into\n\n4 Pi R2.
146689
to find the area of a circle.pie r squared.r being 1/2 dia.
247689
Use analytical trig (hint: sin function).  That should give you the answer you are looking for.
48612
Let r be the radius of the circle and s the length of the square's sides.\ncircle perimeter=2*pi*r, square perimeter=4*s\n2*pi*r=4*s => s=pi*r/2\ncircle area=pi*r^2, square area=s^2\ns^2=(pi*r/2)^2=pi^2*r^2/4\nBut pi<4 => pi^2*r^2/4<pi*r^2 => square area < circle area
930129
r = √1² + (-1)² = √2\nθ = arctan(1/-1) = -π/4 ± n2π, where n is any integer.
19668
The way to figure this out is, \n\nS=segment length of arc \nA=angle subtended by arc\nR is radius of circle \n\nS/A=2*pi*R/(2*pi),\n\nso S=RA\n\nthen differentiate with respect to time t, \n\nand dS/dt=R*dA/dt,\nand dA/dt=w, the angular speed\n\ndS/dt=T, tangential velocity\n\nso T=R*w
1165642
One way to reason is this.  Let n be any even integer greater than or equal to 4.  Divide the circle into n equal wedges (by drawing n/2 diameter lines with angles between successive lines equal to 360/n degrees).  Now, cut the wedges out and make a "rectangle" with them: n/2 wedges with the points downward and the arcs on top of adjacent pairs of wedges touching each other, then the other n/2 wedges with the points upward and adjacent arcs touching, filling the spaces of the first n/2 wedges.  What you end up with is almost a rectangle with top and bottom each made of n/2 360/n-degree arcs, and the lateral sides slanting slightly, made from the long edges of the wedges on each end.\n\nYou can estimate the area of this figure (which is the same as the area of the original circle of radius r) by pretending it IS a rectangle.  The length is the circumference of the circle, or 2*pi*r/2 (since half the circumference is the top, half is the bottom) (by definition of pi).  The width is the length of a wedge, or r.  So the area is about pi*r^2.  \n\nTo turn the estimate into an exact value, consider what happens as n goes to infinity, that is, it increases without bound.\n\nAs n goes to infinity, the slanted edges aproach being verticle and the number of arcs making up the top and bottom approaches infinity, and the arcs themselves approach straight horizontal lines.  Thus, the figure approaches a rectangle of exactly area pi*r^2.  However, for each n, you have the same circle of the same area, so the area of that circle is pi*r^2.