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#1 2016-08-04 15:59:44

anniep418
Member
Registered: 2016-07-28
Posts: 11

Area and Volume of Polygons, Pyramids, and Spheres

..

Last edited by anniep418 (2016-09-05 07:05:47)

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#2 2016-08-04 16:20:24

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Area and Volume of Polygons, Pyramids, and Spheres

Hi;

You must use imgur.com to upload a picture.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2016-08-04 16:34:53

anniep418
Member
Registered: 2016-07-28
Posts: 11

Re: Area and Volume of Polygons, Pyramids, and Spheres

http://imgur.com/a/daDcV

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#4 2016-08-04 17:04:56

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Area and Volume of Polygons, Pyramids, and Spheres

Last edited by thickhead (2016-08-09 16:37:16)


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#5 2016-08-04 19:10:51

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Area and Volume of Polygons, Pyramids, and Spheres

hi anniep418

Welcome to the forum.

Q1,2,3,5 look correct to me.  smile

For Q7.  Looking from above the pool is made up of three shapes: half an octagon at each end and a rectangle joining them.  So the surface area would be the area of an octagon plus a rectangle.  So call the lengths by suitable letters and write out the correct formulas for the areas.  The volume will just be area of the top times the depth of the pool.  It would be more complicated if the pool had a shallow end and a deep end, but the picture shows the pool is a prism and you're told it's full to the top.

Hope that helps,

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#6 2016-08-05 09:34:53

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Area and Volume of Polygons, Pyramids, and Spheres

Hi;

Number 4 just requires you to plug into a formula.

where n is the number of sides. Can you complete your assignment now?

Number 6 has been done several times in here alone.

http://www.mathisfunforum.com/viewtopic … 12#p385612

See post #3.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#7 2016-08-07 19:02:21

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Area and Volume of Polygons, Pyramids, and Spheres

hi anniep418

When it said 'surface area' I was thinking just the area of the water surface.  But I see now it wants the surface area of the liner.  That means you would need to include the area of the sides.  It looks like the sides are made up of equal straight sections so once you've measured one (with a tape measure? do they really want you to say that? smile ) you can multiply by the depth for the area of one, and then multiply by the number of them (8 around the octagon plus 4 making the rectangular sides) to get the total area of the sides.

Add to your answer what 'a', 'l' and 'w' stand for, and introduce a letter for the depth.  Explain the formula for the octagon ... how it is made from triangles etc.  Hopefully that should cover it.

Bob

ps.  Is this from 'CompuHigh' by any chance?


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#8 2016-08-08 00:38:50

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,226

Re: Area and Volume of Polygons, Pyramids, and Spheres

I note you could definitely integrate a volume to find the area/volume of no 7.


The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

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#9 2016-08-09 20:52:03

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Area and Volume of Polygons, Pyramids, and Spheres

hi anniep418

Q2. 

tan(54)=a/5

Right angled triangle!  That should be a/2.5

There are 10 right angle triangles.

The base and height are 'a' and 2.5.  Make sure you're calculating the area of the right triangle.

Q3.  That answer looks ok to me.   You've said 10.609 for one triangle.  Say which triangle that is and put in the steps that lead to that answer.

Q4.  If you call one side 's' then go through what you usually do to calculate the area of one right angled triangle and times by 14.  That will give you an equation that you can solve for s.

Q5.

I split an octagon into 8 triangles with angles of 135deg. Then into right angle triangles of 45-45-90.

You have split the octagon into 8 triangles meeting at the centre.  Good!  360/8 = 45 so the angle at the top of one triangle is 45.  That makes the two equal angles at the base (180-45)/2 = 67.5  So you need to re-calculate this area.  I thought the answer you posted at the start was correct.

Q6.  Here's a diagram.  I think the dotted line is 14, so AD is 7.  You will need to use trigonometry to work out AB.

Jekn9eK.gif

Q7.  From the picture it looks like the pool sides are made from equal length sections.  From one white square to the next is what I mean by a section.  They look to be the same size.  There are 4 around the half octagon at one end and 4 again at the other end.  Between the two half octagons there are 2 sections per side making a rectangular shape in the middle.  If one section is length 's' the the octagon has sides 's' and the rectangle is 2s one way and let's call it W for the width of the pool.  You could measure this separately or, if you wanted to be clever, calculate it using the angles of an octagon.  I suggest the first as less stressful.  Your teacher wants you to put in every step of the method so imagine you're explaining this to a six year old who has got to go out with a tape measure and do the job.  Anything you leave out means your young friend will get stuck with how to complete the task.

Hope that helps,  smile

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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