The best shape of guttering
GCSE Math's Gutter Investigation Introduction The purpose of this investigation is to determine the best shape of guttering taking into account a number of different factors, such as the maximum volume and practicality. The gutters I test, shall all be made from a sheet of plastic twenty-four centimetres by four hundred centimetres, as shall my final choice. I shall test both regular and irregular shapes, these shall include triangles, rectangles, polygons and a semi circle. In order to determine the best shape I shall use Microsoft Excel to produce tables and graphs which shall help me to compare the maximum capacity of each Hypothesis I have some expectations as to what my results will be: "The semi-circle shall have the greatest volume and the more sides a shape has the greater it's volume shall be so long as it is regular" The first shape I shall investigate is the triangle as, according to my hypothesis, it should have the least volume. I will start by placing the possible isosceles triangles into a graph, since it is guttering the triangle need have only two sides. This table and graph shows that a triangle with a ninety degrees angle gives the greatest volume I will now test a scalene triangle to see if the area decreases of increases. Net Width Net Length Side Angle Area Volume 24 400 2 70 2.503 5001.2 24 400 2 60 24.625 9850 24 400 2 50
Fencing Problem - Maths Coursework
Fencing Problem - Math's Coursework A farmer has exactly 1000 meters of fencing and wants to fence of a plot of level land. She is not concerned about the shape of the plot but it must have a perimeter of 1000 m. She wishes to fence of a plot of land that contains the maximum area. I am going to investigate which shape is best for this and why. I am going to start by investigating the different rectangles; all that have a perimeter of 1000 meters. Below are 2 rectangles (not drawn to scale) showing how different shapes with the same perimeter can have different areas. Below is a table of different rectangles. Height Length Area 0 490 4900 20 480 9600 30 470 4100 40 460 8400 50 450 22500 60 440 26400 70 430 30100 80 420 33600 90 410 36900 00 400 40000 10 390 42900 20 380 45600 30 370 48100 40 360 50400 50 350 52500 60 340 54400 70 330 56100 80 320 57600 90 310 58900 200 300 60000 210 290 60900 220 280 61600 230 270 62100 240 260 62400 250 250 62500 260 240 62400 270 230 62100 280 220 61600 290 210 60900 300 200 60000 310 90 58900 320 80 57600 330 70 56100 340 60 54400 350 50 52500 360 40 50400 370 30 48100 380 20 45600 390 10 42900 400 00 40000 410 90 36900 420 80 33600 430 70 30100 440 60 26400 450 50 22500 460 40 8400 470 30
Perimeter Investigation
I will be investigating the shape, or shapes, that could be used to fence a plot of land, which contains the maximum area, using exactly 1000 metres. To start I will be investigating the rectangle family as shown below: From these results, the maximum area using exactly 1000 metres of fencing is the rectangle that measures 250 by 250. Its area is 62500m², which is the biggest area and it is square in shape, which proves that the square is the best to use, when investigating four sided shapes. I have plotted a graph from these results obtained: My next investigation will be using triangles to find the maximum area of land that could be fenced, using exactly 1000 metres. I will be using triangles as shown below: Base/m Sides/m Perpendicular Height/m Area/m² 50 475 474.3 1857.5 00 450 447.2 22360 50 425 418.3 31372.5 200 400 387.3 38730 250 375 353.6 44200 300 350 316.2 47430 350 325 273.9 47932.5 400 300 223.6 44720 450 275 158.1 35572.5 From these results, the maximum area using exactly 1000 metres of fencing is the triangle that measures, base 350m, sides 325m and an area of 47932.5m². This triangle is the best to use when investigating 3 sided shapes, because it has the biggest area and a perimeter of 1000 metres. I decided to use regular shapes through-out my investigation because only regular shapes, i.e. shapes with equal
1,000m of fence - what is the maximum area I can enclose?
,000m of fence - what is the maximum area I can enclose? Introduction: In this project, I am trying to find out the maximum area of an enclosure I could make with 1000m of fencing. I am going to attempt to tackle the problem by using different shapes, Including Quadrilaterals, Pentagons, Hexagons, Octogons, Isogons and circles. I already know that the mathematical solution (circles) may not be useful for the farmer because circles do not tessellate. The plots need to tessellate to make use of as much land as is possible - I have shown examples of tessellation below: Historically, farmland in Britain was divided into hexagonal plots to use all available space. Since proper roads were built, this has no longer been possible, as space is at a minimum and roads usually run at the sides of fields. Hypothesis: My hypothesis is the more sides a shape has the more area it will contain and I believe the mathematical solution will be a circle because circles have infinite sides. Logical Ideas for shapes: * Triangle * Quadrilateral * Pentagon * Hexagon - There is a pattern here, so I will jump to: - * Decagon (10 sides) * Isogons (20 sides) * n number of sides How do I know if a Formula Measures Area or Volume? /2 b h measurement x measurement l b w measurement x measurement x measurement Quadrilateral: As with triangles, there are different types of
Acoustics Assignment
Acoustics Assignment Assignment Brief To choose a room and analyse the construction materials and subsequent surface areas of that room, and using the given formula, show an understanding in the calculations involved in solving absorption coefficients, reverb times and standing waves of any given space. Introducing Acoustics Before any formula can be applied, or calculations analysed, a firm understanding must be grasped of the main components involved in this assignment, namely: Standing waves Nodes / Anti-nodes Fundamental frequency Reverberation time Absorption Absorption coefficients Frequency Wallace Sabine Let us consider each heading Standing Waves The modes of vibration associated with resonance in extended objects like strings and air columns have characteristic patterns called standing waves. These standing wave modes arise from the combination of reflection and interference such that the reflected waves interfere constructively with the incident waves. An important part of the condition for this constructive interference is the fact that the waves change phase upon reflection from a fixed end. Because the observed wave pattern is characterised by points, which appear to be standing still, the pattern is often called a 'standing wave pattern.' Nodes / Anti-nodes One characteristic of every standing wave pattern is that there are points along the
The aim of this coursework is to investigate which shape gives the largest enclosed area for a fixed perimeter of 1000m. In the coursework I will be investigate different shapes with different number of sides to see which encloses the largest area.
Jugdeesh Singh Maths Coursework 2003 Mrs Phull 0 Blue Aim The aim of this coursework is to investigate which shape gives the largest enclosed area for a fixed perimeter of 1000m. In the coursework I will be investigate different shapes with different number of sides to see which encloses the largest area. Three sided shape Triangle The only three sided shapes are triangle. There area depends on the length of each side. For the triangle I will be investigating which triangle with has the largest area by changing the lengths of each side and eventually getting the triangle with the largest area. Prediction: I predict that the triangle with equal sides will have the largest area. This is the equilateral triangle. First I will start by changing the length of the base. To calculate the area of the triangle I will be using the following formula /2 Base x Perpendicular Height E.g. /2 Base x Perpendicular Height (1/2 x 10m) x 15m = 5m x 15m = 75 m2 For some triangles the perpendicular height is not given, therefore we have to work the height out our selves. We will do this by applying Pythagoras' Theorem, which is. The square on the hypotenuse is equal to the sum of the squares on the other two sides. a2 + b2 = c2 E.g. At this point we do not know the perpendicular height so by using Pythagoras' Theorem we can work out the height, but first we must divide the
t shape t toal
T-Total Part 1 The aim of the investigation is to find out the relationship between the t-number and t-total. The t-number is the number in the t-shape, which is at the base of the T. The t-total is the sum of all numbers inside the t-shape. I will start my investigation by looking at t-shapes on a 9 by 9 grid. To solve the problem of finding the relationship between the t-number and t-total I will look at the information algebraically. I will firstly assign a letter to the t-number of the shape, this letter will be T. I will then express the rest of the numbers in the t-shape with the letter assigned to the t-number in the t-shape. Therefore it will give me a standard expression to apply to all the t-shapes. Where the expression is equal to the t-total. Examples ` The expression works for all t-shapes in a 9 by 9 grid. I will now simplify the expression into a simple formula. T + (T-9) + (T-17) + (T-18) + (T-19) = T-total 5T - 63 = T-total I will see if this new formula still works. 5 ? 20 - 63 = T- total 00 - 63 =T - total 37 = 37 5 ? 21 - 63 = T- total 05 - 63 = T - total 42 = 42 Part 2 I will now as part of my investigation use different grid sizes, transformations of the t-shape and investigate the relationship between both. Then I will see how the t-number and the t-total relate to the new factors. The smallest grid size can only be a 3 by 3 grid
Take ivy leaves from the North and South side of a hedge to come to the conclusion of what natural factors will effect the ivy leaves and why.
B3: WHAT AFFECTS THE LEAVE SIZE OF IVY? AIM: To take ivy leaves from the North and South side of a hedge to come to the conclusion of what natural factors will effect the ivy leaves and why. THEORY: The main factors that will affect the ivy leaves are how much sunlight the ivy gets, which I will be concentrating on in my investigation. Industrial factors would affect the ivy but the hedge we are taking them from this would not have any noticeable affects. PREDICTION: I predict that the ivy leaves that have more sunlight will be of a smaller size because if they get more sunlight they don't need as much energy that is taken from the sun. Meaning that they have a smaller leave surface area. Some people might think that if they get more sunlight they will be larger because it is easier to get energy from the sun and that it can grow bigger with the energy it gets from the sunlight. I also think that the ivy leaves that are in the shade most of or all the day will be larger because they do not get as much energy from the sun as the ones on the other side so it they do ever get sun light they will have to be bigger so they can take in as much energy as possible. Other factors which might affect my results is the kind of tree the ivy has grown up because of how much nutrients and minerals it is getting from the ground. I will prevent this from interfering by taking it from
Maths GCSE Courswork
Introduction A farmer has exactly 1000 metres of fencing and wants to fence off a plot of level land. She is not concerned about the shape of the plot, but it must have a perimeter of 1000m. So it could be or anything with a perimeter (or circumference) of 1000m. She wishes to fence off the plot of land which contains the maximum area. Investigate the shape, or shapes, that could be used to fence in the maximum area using exactly 1000 metres of fencing each time. Triangles I will start the investigation with triangles. The triangle is one of the basic shapes as it has only three sides to it. I will calculate the maximum areas for two types of triangles: > Equilateral Triangle > Isosceles Triangles An equilateral triangle is a triangle with all three of its sides the same length. An isosceles triangle is a triangle which has two of its sides the same length and the other is different. It is usually the base of an isosceles triangle which has a different length to the other two sides. Here are some of the formulae I will need to find the maximum areas of each triangle: > Area: base x height / 2 > Pythagoras Theorem: a2 + b2 = c2 > Heron's Formula: Equilateral Triangle This shape has a perimeter of 1000m: Perimeter = 333.33 + 333.33 + 333.33 = 1000m I will need to use the formula base x height/ 2 to calculate the area of triangle but in this case and every
Is there a connection between the size (surface area) of a leaf and the between the trunk to the road?
Surface Area of leaves Research question: Is there a connection between the size (surface area) of a leaf and the between the trunk to the road? Aim: To find a connection between the size(surface area) of the leaf and the distance between the trunk and the road. Hypothesis: Yes, I believe that the surface area of the leaves will increase the further away from the road they are. I believe that there are many reasons all due to different pollutions, caused by the cars driving on the road. I'm sure that it affects the leaves in other ways such as premature leaf drop, delayed maturity, plant growth, reproduction....but also the size will get affected. Cars are responsible for a tremendous amount of air pollution and wasted energy that affect humans and our environment. Acid rain, which is caused by air pollution, poisons our water as well as plants. The smoke and fumes from burning fossil fuels rise into the atmosphere and combine with the moisture in the air to form acids rain. The main chemicals here are sulphur dioxide and nitrogen oxides. The tree's roots absorb water from the ground, as a life source and when the acid rain, rains around that tree its life source is poisoned. The acid rain also harm the leaves as fog, acid fog, which the leaves will bath in, and that will make their protective waxy coating can, wear away. Which could lead to water loss, which makes the