The slant height of a right circular cone is 10 and it's total areaiis 144pi, what is the radius?
467313
ok , so you should have the equation for the right circular cone -\n\nthe area of the side of the cone — equals the circumference of the base circle multiplied by the slant height of the cone (the distance from the apex to any point on the outside of the base).\n\nNow - if the Slant height is 10 and the total area is 144 pi (square units) then it is simply a matter of substituting into the equation\n\nArea = Circumference * Slant Height\nArea of a Circle = Pi*(Radius^2)\n\nSo, what do you know?\n144 = (3.1415926* Radius^2)*10\nYou ought to be able to solve this equation for R^2.\n\nI do not believe in giving all of the answer to the homework assignment - I hope this helps you.
529200
Good that you care to ask. The answer to this should be evident to you by integration (hope you have been introduced to calculus? If not, you will be this year.). \n\nI assume that you don't have much of a background.\n \nOK, let the cone be such that its height is H, base radius R. \n\nWhat you need to do is consider an infinitesimally thin section of the cone (a diagram should be so helpful here, unfortunately not possible) at height h from the bottom and of height (along the axis) 'dh', such that the radius of the section is a uniform 'r'. \n\n(Note that you have a uniform radius r to the section because you have chosen a very thin section of the cone.)\n\nNow, the surface area of the section considered is \n2*pi*r*dh*cosec x. (x is the cone half-angle)\n\nThe cosec term comes from basic trigonommetry, when you realise that the section is tilted and not exactly parallel to the axis. \n\nThe surface area  of the entire cone, indeed the curved surface area, is a summation of all such infinitesimal sections, each of surface area 2*pi*r*dh* cosec x \n(where r is the radius of each section). \n\nThis above sum can be found by \nintegrating 2*pi*r*dh*cosec x (that is a word in the language of calculus for finding out the sum of many small parts) over the entire height of the cone. \n\nalso realise that r = h tan x. \n\nso an integration of 2*pi*htan x*cosecx*dh gives us,\n\nCSA = 2*pi*sec x* (H^2/2)  \n    = pi*R* H (sec x/tan x)\n    = pi*R* H cosec x\n    = pi*R*L\n\nHope this satisfies.
919807
I can't find anywhere that says exactly on this.  However I could find that it tops out at about 600m above the surrounding planes.  Also it is aprox 3000m in diameter.  So if it is a perfect cone, which it is not, it would be 14,681,680 square meters surface area.  Not sure how much this helps you.
970422
The solution is too convoluted to put it here without diagrams and a good equation editor.  If you wish, I can email a Word document detailing the solution.  I figure that the cone is (1 + 2*sqrt(2/3) + sqrt(3))*r (about 4.365 r) high and has a base radius of ((sqrt(1/2) + sqrt(4/3) + sqrt(3/2))*r or about 3.087.
692007
its quite simple the radius is half way threw the circle so its the radius 3 squared which equals 9 and 9 times pi or 3.14 equals 88.7364 but u mite have to round it so if u round to a whole number it would be 89 but to the nearest tenth it would be 88.7
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
72316
The area of circle is pi*r^2 (pi r square). Now let the increased radius be R and iniitial radius be r.\nArea after expansion  =pi*R^2 (pi R square)\nArea before expansion =pi*r^2 (pi r square)\nIncrease in area      =pi*R^2  - pi*r^2\n                      =pi(R^2 - r^2) \n                      =pi(R+r)(R-r)\n                      =3*(7+5)(7-5), taking pi=3 aprox.\n                      =3x12x2\n                      =72 approx.\n Since answer c alone is near to this value the answer is C.\n\nThough the steps given are more the problem is done mentaly and not by writing these steps. The steps in mental calculations are \n1. 7+5=12\n2. 7-5=2\n3. 3x12x2=72 and choose the answer.
554282
A = base * height\n\nbase = 8\n\nslant height = 6\nto get the actuall height, we use trig\n\nthink of 6 as the hypotenuse\n\nsin 30 = height / slant height\n\nor height = sin30 * 6\n\nheight = 3\n\ntherefore area = 8 * 3 = 24
838513
Sigh - first guy had it right, but didn't explain it all.  \nPi = 3.14- all you need for the problem\nRadius= half the diameter of your circle. You find the midpoint and measure from there to the side of the circle, in any direction. Most problems give you the radius. or at least show you the midpoint on the circle.\n\nSo, it is 3.14 x the amount of the radius x 2= the area of the circle.\n\nYou can do this in reverse as well, if you know the area but not the radius.
934101
what's the height?  you need the height to finish this problem\nwhat type of shape is it?  a cylinder? cone?\nbe specific or no one can help you
513696
The area equation of a circle is pi r^2. And, a circle has an arc measure of 360. Since the shaded region has that of 40, it would be 40/360 = 1/9 of a circle.\nA = 1/9 pi r^2 = 59\npi r^2 = 59 x 9\nr^2 = 59x9/pi\nr = sqrt 59 x 9/pi = 13! =)
625973
How to do this problem:\n1. Find the Radius. To do this, take the diameter and divide by two. This gives you a radius of 5.\n2. Because the Area of a circle is equal to Pi times the radius squared, and your teacher wants the answer in terms of pi, square the radius and get 25 pi.
952353
The curved surface area is 2*pi*r*h\n\nor 2*3.142*27*12 sq cms\n\nand 2*3.142*17*35 sq mms\n\nyou can do the rest
667615
I'm sorry, miscalculated\nArea of a Circle= pi r^2\n3.14 x (5)^2\n3.14 x 25\nArea of the Circle is 78.5 meters
999585
I knew it as I did the activity.Draw a circle an divide it into 8 equal parts.It should be equal.Then cut it and stick such that the tip of one cone is up and the other is down.See that the edges stick each other close together.Do it until you finish all the 8 parts.\nNow you needed some concentration.You can see that it forms a parallelogram.Now area of parallelogram=base*height and the circumference of circle=Pi*2*radius.The base of the diagram is half the circumference that is Pi*radius,and the height will be the radius.You will also notice that Area of parallelogram=Area of circle.Therefore,Base*height=Pi *Radius *radius.so, now you have got pi*radius square.\nHope you like my answer.
919539
Area =pi (Radius)^2 = 22/7(3)^2 =22(9)/7 = 28.29 ft^2 Ans.
802377
Assume that the sphere is centered at (0,0,0)\nStart out by slicing the sphere through its center and looking at the cross section of the sphere and the cylinder. You will have a rectangle inscribed inside a circle.\n\n\nDraw a line from the center of the rectangle to the corner of the rectangle that is in the first quadrant. It will have length r since it is a radius of the sphere.  Let t be the angle the radius makes with the positive x axis. \n\nThe height of the cylinder is   r*sin(t).\nThe radius of the cylinder is r*cos(t)\n\nThe surface area is 2*pi*r^2cos^2(t) + 2*pi*rcos(t)rsin(t)\n\nTake the derivative and find the max.