jyoticlub Posted June 18, 2005 Share Posted June 18, 2005 Please solve the problem in detail The height of the cone is 30cm.A small cone is cut off at the top by a plane parallel to base.If its volume be 1/27 of the volume of the given cone, at what height above the surface the section made? Thanks Link to comment Share on other sites More sharing options...
Newtonian Posted June 18, 2005 Share Posted June 18, 2005 1cm Link to comment Share on other sites More sharing options...
mezarashi Posted June 18, 2005 Share Posted June 18, 2005 Describe the volume of the little cone and large cone in terms of its dimensions (r, height). Add in the variable y which is the height in which you are going to cut it at. Then set the condition: Small cone volume = 1/27 Large cone volume And solve from there. Link to comment Share on other sites More sharing options...
albertlee Posted June 18, 2005 Share Posted June 18, 2005 the big cone volume = (pi)r230 * 1/3 = (pi)r210 what is the ratio of its height to volume? 30cm : (pi)r210 cm3 which is: 3cm : (pi)r2 cm3 note that the height of the maller cone is directly proportional to its volume. what's the volume of the smaller cone? big cone volume / 27, right? therefore, is: (pi)r210 cm3 / 27, which is: (pi)r2(10/27) cm3 the height thus will be, according to the ratio of height and volume, 3 / (pi)r2 * (pi)r2(10/27) = 3 * 10/27 = 30/27 cm Albert Link to comment Share on other sites More sharing options...
Primarygun Posted June 18, 2005 Share Posted June 18, 2005 I don't get this answer. .......... Link to comment Share on other sites More sharing options...
albertlee Posted June 18, 2005 Share Posted June 18, 2005 PrimaryGun, is this the reason you send me a PM with a 'hi'?? Link to comment Share on other sites More sharing options...
greentea Posted June 19, 2005 Share Posted June 19, 2005 20 cm v1,h1,r1=v,h,r smal cone v2,h2,r2=v,h,r big cone v1=h1*(r1)^2*pi/3 v2=h2*(r2)^2*pi/3 h1/h2=r1/r2 (similar triangles) x (required height)=h2-h1 v1/v2=1/27=(h1/h2)^3 =>h1/h2=1/3 x=30-10=20 Hope that is detailed enough. Link to comment Share on other sites More sharing options...
DQW Posted June 19, 2005 Share Posted June 19, 2005 Phew ! At least someone got the answer right. But why are folks providing complete (at least one person has) solutions, when the OP has shown no original effort ? To the OP : Please show anything that you have tried or any ideas you have. You won't gain much by having others do your homework for you. Fortunately, there are enough wrong answers here that the correct solution is not yet revealed. What do you think are the steps you must take; and what important properties must you take advantage of ? To Dave/matt : Is this kind of thing the norm here ? Link to comment Share on other sites More sharing options...
Dave Posted June 19, 2005 Share Posted June 19, 2005 Not usually, no. However, people had already posted complete solutions before I had a chance to survey the thread, so I couldn't really do much about it then. Link to comment Share on other sites More sharing options...
greentea Posted June 19, 2005 Share Posted June 19, 2005 alright, I am not gonna do people's HW again, just give hints/suggestions. new here. Link to comment Share on other sites More sharing options...
the tree Posted June 19, 2005 Share Posted June 19, 2005 A small cone is cut off at the top by a plane parallel to base.From that you know that they are mathmatically similar, the shape is the same, but the scale isn't.If its volume be 1/27 of the volume of the given coneIf it's volume is 1/27 then it is 1/27 of the larger cone in volume and dimensions and any other mesurement you care to take. That's all you need to know. You can do the number crunching yourself, that should be easy. Link to comment Share on other sites More sharing options...
albertlee Posted June 19, 2005 Share Posted June 19, 2005 Hmm, guess my answer is wrong, for 30- 30/27 cm...... Link to comment Share on other sites More sharing options...
greentea Posted June 19, 2005 Share Posted June 19, 2005 It is more like 30 - 30/(27^1/3) since height is one-dimensional, while volume is 3D. If it is simpler think of a cube. 8 times bigger volume means only twice the side. Same with any figure that is scaled. Link to comment Share on other sites More sharing options...
abeefaria Posted June 21, 2005 Share Posted June 21, 2005 I simply set V1 = 27(V2) and got an answer of 1.111, same as albert. That is to say, the cut needs to be made 1.1111 cm below the tip. Link to comment Share on other sites More sharing options...
Primarygun Posted June 21, 2005 Share Posted June 21, 2005 PrimaryGun, is this the reason you send me a PM with a 'hi'?? Yes, I got 20cm by concerning the cones are in similar shape. Link to comment Share on other sites More sharing options...
jyoticlub Posted June 21, 2005 Author Share Posted June 21, 2005 Well , Thanks everybody for your efforts. I now should keep in mind to provide things i know before posting a new thread. Well the correct answer is 20cm. Thanks Link to comment Share on other sites More sharing options...
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