Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    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
    • Thread Starter
    Offline

    0
    ReputationRep:
    also, how would i use calculus in a piece of coursework like this?

    (Original post by 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?

    (Original post by 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

    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?

    (Original post by 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?

    (Original post by 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.

    (Original post by 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?
    • Thread Starter
    Offline

    0
    ReputationRep:
    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.
    • Thread Starter
    Offline

    0
    ReputationRep:
    ...
    • Thread Starter
    Offline

    0
    ReputationRep:
    :confused:

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

    Ben
    • Thread Starter
    Offline

    0
    ReputationRep:
    :mad: :confused:
    • Thread Starter
    Offline

    0
    ReputationRep:
    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

    (Original post by 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
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by 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

    (Original post by 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
    • Thread Starter
    Offline

    0
    ReputationRep:
    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

    (Original post by 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.

    the best area I have got for a rectangle is 56.25cm^2
 
 
 
Turn on thread page Beta
Updated: October 22, 2003

University open days

  • University of Lincoln
    Mini Open Day at the Brayford Campus Undergraduate
    Wed, 19 Dec '18
  • University of East Anglia
    UEA Mini Open Day Undergraduate
    Fri, 4 Jan '19
  • Bournemouth University
    Undergraduate Mini Open Day Undergraduate
    Wed, 9 Jan '19
Poll
Were you ever put in isolation at school?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Equations

Best calculators for A level Maths

Tips on which model to get

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.