• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Maths Investigation: Drainage Channels.

Extracts from this document...


Maths Investigation: Drainage Channels. We have been given a length of metal that is 60cm wide. What shape should the metal be bent into so it will hold the greatest volume of water? 60cm X cm X cm Conditions: 1. You must have a symmetrical cross section. 2. The channel must be widest at the top. Semicircle The circumference of the whole circle would be 120cm but the circumference of the semicircle would be 60cm. 120 = 2?R 60 = ?R R = 19.1cm Area = ?R� A = ??x 19.1� A = ? x 3364.76 A = 1145.92 1145.92 is the area of the whole circle so the area of the semicircle is half of that. ...read more.


224.88cm� Example 2 Sin10� x X/30 X = 0.174 x 30 X = 5.21 Cos10� x h/30 H = 0.98 x 30 H = 29.54 Area = 5.21 x 29.54 = 154.0597cm� As you can see this is a long drawn out process, so if we were to create a table it would save having to draw all the triangles out. This is on the next page Rectangles X X 60 - 2X Example 1 5cm 5cm 50cm Area = 50 x 5 Area = 250cm� Graph of results on next page. Trapeziums. 20cm 20cm 20cm 20cm 20cm Opp xcm Adj Hyp H 50� 20cm Sin50� = x/20 X = 20sin50 Cos50� = h/20 H = 20cos50� Instead of doing this drawn out process I found a formula that worked, it is Area = (a+b/2) ...read more.


X 20 X S Z H H Z S B X H Z S SinZ = x/s X = s x sinz� Cosz = h/s H = S x cosz Area = b + (b + 2s sinz�)/2 = Ans Area = Ans x 20cosz� There are graphs on the next few pages to represent these results. (To enter these results into a spreadsheet I needed to know about radians which is how a spreadsheet works.) 2 x 3.142 = 360� 1� = 3.142/180� N Sides 180/n 60/n 36� Side = 60/n Angle = 180/n 180/n 90/n A H O 30/n TOA CAH SOH (Tan 90/n = 30/n) /h h = (30/n) / tan 90/n Area = 30/n x (30/n) /tan 90/n = 30/n x 30/n tan 90/n Formula for Area is = 900/ (n x tan 90/n) ...read more.

The above preview is unformatted text

This student written piece of work is one of many that can be found in our GCSE Fencing Problem section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Fencing Problem essays

  1. Fencing investigation.

    tan (360�2n) To work out the area of 1 triangle is: 1000�2n x 1000 tan (360�2n) 2n To work out the area of the whole pentagon is therefore: 1000�2n x 1000 n x (tan (360�2n) 2n ) This whole thing can be simplified to: 500�n x 500 n x (tan (180�n)

  2. Graphs of Sin x, Cos x; and Tan x

    cos B or, c2 = a2 + b2 - 2ab cos C These formulae can be rearranged to give: Check whether your formula sheet gives these formulae in both formats. If it doesn't, you may need to rearrange them yourself!

  1. Geography Investigation: Residential Areas

    I have chosen this method for collecting data about the intangibles of the areas because it is changing feeling into numbers so it can be used to create graphs and charts - this will help me to evaluate the area in a visual way.

  2. Fencing - maths coursework

    = 500m 500 x 50 x 50 x 400 =22360.68m2 450m 450m 100m S= 0.5 (450m + 450m + 100m) = 500m 500 x 50 x 50 x 400 250.5m 250.5m =22360.68m2 499m S= 0.5 (499m + 250.5m + 250.5m)

  1. Borders Investigation

    These differences should form a linear sequence, of the type encountered when looking at perimeter, from which a formula can easily be derived. This linear formula, when added to the , will give the overall formula for the nth term of the area sequence.

  2. Tubes Maths Investigation

    Also the square has a larger volume than all the cuboids suggesting that regular shapes give larger volumes. The results for the cuboids with a 32cm base are shown on the graph on the following page. This graph shows a gradual rise up to when the tube is a regular

  1. Biological Individual Investigation What Effects Have Management Had On Grasses In Rushey Plain, Epping ...

    + Light + Carbon Dioxide � Glucose + Oxygen The carbon from the carbon dioxide is used to build up complex organic molecules, which are used to build up cell components, and enable the plant to grow. Photosynthesis relies on the following conditions: * Light * Water * Carbon Dioxide

  2. Fencing Problem - Math's Coursework.

    Reproduction or retransmission in whole or in part expressly prohibited 435 430.116 27957.540 140 430 424.264 29698.480 150 425 418.330 31374.750 160 420 412.311 32984.880 170 415 406.202 wwdf dfw stdfdfud edf dfnt cdf endftral dfcodf uk. 34527.170 180 410 400.000 36000.000 190 405 393.700 37401.500 200 400 387.298 38729.800

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work