Maths coursework crisis

hi, i no that a semi circle of circumference 30cm has a better surface area that any shape (is this right, and there's only 1 possible best area int there?), but ive tried half an octangle by splitting it up into two rectangles n two isoceles trinagles but i got a better answer, ive checked thru it but i cant see where ive gon wrong

Rec 1 height 5.303300859
Rec 1 width 7.5
Area rec 1 39.77475644

Tri side 1 7.5
Tri side 2 5.303300859
Tri side 3 5.303300859
Tri-angle a 45 deg
Tri-angle b 90 deg
Tri-angle c 45 deg
Area 2 tris 39.77475644

Rec 2 height 3.75
Rec 2 width 18.10660172
Area rec 2 67.89975644
Total area 147.4492693

whereas on my semio-circle, i only got 143.23945

any help at all is apprecia8d guys

Reply 1

leeds_lad_luke

OP

also, how would i use calculus in a piece of coursework like this?

Reply 2

Unregistered

leeds_lad_luke

also, how would i use calculus in a piece of coursework like this?

You'd use optimisation to find the largest possible value, although you've made it tricky for yourself.
Do you really need to use calculus at GCSE?

Reply 3

Unregistered

leeds_lad_luke

also, how would i use calculus in a piece of coursework like this?

well I think a circle has the largest area, not the semi-circle

Reply 4

Unregistered

also, if you are talking about 2D (i.e. just the area of the shape), try to prove why a regular shape has the largest area. e.g. a rectangle and a square, both having a perimeter of 30cm, why does a square have the largest area?

Reply 5

Unregistered

You'd use optimisation to find the largest possible value, although you've made it tricky for yourself.
Do you really need to use calculus at GCSE?

what do you mean by optimisation, trying possibilities one by one?

Reply 6

Unregistered

garytse86

also, if you are talking about 2D (i.e. just the area of the shape), try to prove why a regular shape has the largest area. e.g. a rectangle and a square, both having a perimeter of 30cm, why does a square have the largest area?

ook. I took "surface area" to mean 30 + 30pi. (eg perimeter) because of the guttering example.

Reply 7

Unregistered

ook. I took "surface area" to mean 30 + 30pi. (eg perimeter) because of the guttering example.

try figuring out why a regular shape has the largest surface area?

Reply 8

leeds_lad_luke

OP

hi again, gary, i'm doing half shapes just like a gutter. The aim of the investigation is to find out why house gutters are semi-circular. Our teacher has told us that semi-circles will have the best area.

I have done a rectangle i.e a perimeter of 30cm as below. Its best area was 112.5

|_________|

I have also done a trapezium(using optimisation on excel) (half-hexagon) to find my best area was 129.

Befoe i did my half octagon and half decagon i decided to skip to a semi-circle to get my area of 143.23945cm

I then did my half octagon (at the top of this page) to find my first area was higher than that of the semi circle.

I have just done my half-decagon by splitting it up into triangles and my area was well over 170cm!

I cant see where i am going wrong, (assuming i am right in thinking that there is only one area for a semi-circle with 30cm circumference.)

How could i do an oval????

i have never done calculus b4 btw. But i was just wandering as i have seen other people in my year group from another class use it.

What does it do and how could i apply it to my coursework?
When you said optimisation, did you mean as in improving the area all the time i.e(changing the angle aroung the measurements and vice versa) because i have done that with my trapezium.

I havent done it on my octagon as my first area didn't seem right.

I know thats a lot, but i hope it clarifys it 4 u.
I appreciate your help very much. Thanks.

Reply 9

leeds_lad_luke

OP

...

OP

What exactly is your investigation? What's a 'better' surface area (a larger one?) and compared to what?

Ben

OP

OP

ye a larger surface area

aim is 2 find why house gutters are semi-circular

so id investigate squares, trapeziums, (half hexagon, half octagons n half decagons

Reply 14

Unregistered

leeds_lad_luke

ye a larger surface area

aim is 2 find why house gutters are semi-circular

so id investigate squares, trapeziums, (half hexagon, half octagons n half decagons

All the shapes you've mentioned are 2D, but a gutter is 3D. Are you talking about cross sections and the area of 'air' that's in the cross-section, or the actual surface area of material required to make the 3D gutter shape (semi-cylindrical hollow thing)?

Ben

Reply 15

leeds_lad_luke

OP

Unregistered

All the shapes you've mentioned are 2D, but a gutter is 3D. Are you talking about cross sections and the area of 'air' that's in the cross-section, or the actual surface area of material required to make the 3D gutter shape (semi-cylindrical hollow thing)?

Ben

We're just finding the surface area not the volume

Reply 16

Unregistered

leeds_lad_luke

We're just finding the surface area not the volume

That didn't help me, much - the surface area of what? The cross section? How do you compare different shapes, such as a square and a semi-circle?

Ben

Reply 17

leeds_lad_luke

OP

just the area of the 2d shapes!!!! we're just seeing which shape has the biggest area. The cross-section if you want to put it that way.Not the volume , just the area. e.g length * width

Reply 18

Unregistered

leeds_lad_luke

just the area of the 2d shapes!!!! we're just seeing which shape has the biggest area. The cross-section if you want to put it that way.Not the volume , just the area. e.g length * width

Sorry I don't see how a four-sided shape of perimeter 30cm can have an area of 112.5cm^2.

Reply 19

Unregistered

the best area I have got for a rectangle is 56.25cm^2

Maths coursework crisis

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