# Mensuration

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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

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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?

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The boiler shell is 5 meters long. Sorry for any cunfusion

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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 its 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

 after much thought, I dont think the above method will work for a circular cross section, itll only work with a rectangular one. I think youll need Trig for this, and I can`t help there, ask Dave

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have a look at Circumradius in here: http://mathworld.wolfram.com/topics/TriangleCircles.html

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Would you tell me whether its shape like a part of a sphere?

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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

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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

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aha Chord! I never thought of using string and measuring it that way!

Nice One Dave )

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No problem, just hope that it's the correct interpretation of the question.

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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.

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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.

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Thanks again Dave. The answer i came up with was 5492.19 squared cm. Is it possible for you to verify that.

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I'll verify it in a bit, just going to the pub for my lunch.

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