operator Posted June 29, 2004 Share Posted June 29, 2004 Can anyone help me with this one. A horizontal boiler shell is 150 cm in diameter and 5m long. It is filled with water to a depth of 100 cm. What is the area of the segment of the end plate above the water line? I'm not sure where to begin with this one. Do i have to find the Areas of the Circle, Sector and the triangle and then subtract the triangle area from the sector area to get the area of the segment? If so how do i find the triangle area, what numbers do i use? Am i even going in the right direction with this one? Thanks in advance Link to comment Share on other sites More sharing options...
QuarkQuarkQuark2001 Posted June 29, 2004 Share Posted June 29, 2004 Can anyone help me with this one. A horizontal boiler shell is 150 cm in diameter and 5m long. It is filled with water to a depth of 100 cm. What is the area of the segment of the end plate above the water line? I'm not sure where to begin with this one. Do i have to find the Areas of the Circle, Sector and the triangle and then subtract the triangle area from the sector area to get the area of the segment? If so how do i find the triangle area, what numbers do i use? Am i even going in the right direction with this one? Thanks in advance Sorry, what does 5m long mean? Link to comment Share on other sites More sharing options...
operator Posted June 29, 2004 Author Share Posted June 29, 2004 The boiler shell is 5 meters long. Sorry for any cunfusion Link to comment Share on other sites More sharing options...
YT2095 Posted June 29, 2004 Share Posted June 29, 2004 find the Total volume of the boiler as a cylinder first. you know that if the water comes up to to half way of the end circle diameter 75 cm in your example that the remaining half will be half the total volume since the dia is 150cm. so it`s 100/150 = to get your unit as a function of percent. then multiply that by the water level (100 in your example) that will give you the percentage full. then simply subtract that from your total cylinder volume to get your answer [edit] after much thought, I don`t think the above method will work for a circular cross section, it`ll only work with a rectangular one. I think you`ll need Trig for this, and I can`t help there, ask Dave Link to comment Share on other sites More sharing options...
YT2095 Posted June 29, 2004 Share Posted June 29, 2004 have a look at Circumradius in here: http://mathworld.wolfram.com/topics/TriangleCircles.html that or maybe one of the others listed may help you Link to comment Share on other sites More sharing options...
QuarkQuarkQuark2001 Posted June 29, 2004 Share Posted June 29, 2004 My english is bad, but I really want to help you. Would you tell me whether its shape like a part of a sphere? Link to comment Share on other sites More sharing options...
YT2095 Posted June 29, 2004 Share Posted June 29, 2004 imagine a circle 150cm diameter, then cut across it in a straight line about 2/3 from the edge, like a D shape, what is the area of the smallest part? if that helps you Link to comment Share on other sites More sharing options...
Dave Posted June 29, 2004 Share Posted June 29, 2004 Can anyone help me with this one. A horizontal boiler shell is 150 cm in diameter and 5m long. It is filled with water to a depth of 100 cm. What is the area of the segment of the end plate above the water line? I'm not sure where to begin with this one. Do i have to find the Areas of the Circle, Sector and the triangle and then subtract the triangle area from the sector area to get the area of the segment? If so how do i find the triangle area, what numbers do i use? Am i even going in the right direction with this one? Thanks in advance From what I can see, you don't even have to work out the volume of the thing, so I'm not quite sure why they gave you the height. Basically, you make a chord that is 25cm away from the radius. Then draw a line from the centre of the circle to each point where the chord meets the circle - forming an isoceles triangle, since both of these lengths are radii. Then if you draw a line down the middle, you know this line will be 25cm long (because the chord is 25cm away from the centre of the circle) and you know the hypoteneuse. By Pythagarous you should be able to work out half the length of the chord and hence the area of the chord. I'll draw a diagram if you can't get it Link to comment Share on other sites More sharing options...
YT2095 Posted June 29, 2004 Share Posted June 29, 2004 aha Chord! I never thought of using string and measuring it that way! Nice One Dave ) Link to comment Share on other sites More sharing options...
Dave Posted June 29, 2004 Share Posted June 29, 2004 No problem, just hope that it's the correct interpretation of the question. Link to comment Share on other sites More sharing options...
operator Posted June 30, 2004 Author Share Posted June 30, 2004 Thanks guys for your help, For some reason i can't wrap my brain around this one. Dave would you mind drawing a diagram. Thanks again muchly appreciated. Link to comment Share on other sites More sharing options...
Dave Posted June 30, 2004 Share Posted June 30, 2004 Thanks guys for your help, For some reason i can't wrap my brain around this one. Dave would you mind drawing a diagram. Thanks again muchly appreciated. Okay, here we go. Imagine that my attached image is one of the ends of the tank. Now if I'm interpreting the problem correctly, the area you want to find is the chord AB. You know OC is 25cm long since the radius is 75cm long and you're going from the radius to C, which is the middle of chord AB. Now OA and OB are both radii, making triangles OCB and OCA of equal area. You know the hypoteneuse and the "height" of the triangle, you just need to find the base to find the area of the triangle. Once you've done that, it's pretty easy to find the area of the segment, subtract twice the area you've found and you'll have your answer. Link to comment Share on other sites More sharing options...
operator Posted June 30, 2004 Author Share Posted June 30, 2004 Thanks again Dave. The answer i came up with was 5492.19 squared cm. Is it possible for you to verify that. Link to comment Share on other sites More sharing options...
Dave Posted June 30, 2004 Share Posted June 30, 2004 I'll verify it in a bit, just going to the pub for my lunch. Link to comment Share on other sites More sharing options...
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