Finding Volume Prisms and Pyramids

Finding volume can sound very difficult but it is rather simple if you understand two formulas. The first formula is finding volume for a prism (V=AbaseXh); volume of the area of a base time the height of the objects. For example: The base of this prism is 3.0×2=6 cm^2. After finding the area of the base we can take 6 squared centimeters and multiply it by 5cm giving us 30 cubed centimeters. That is how you find the volume of a prism.

To find the volume of a pyramid we need to know a different formula.This formula is V=1/3pir^2h (1/3 pi time the radius squared time the height). For example a pyramid with a radius of 6cm on the base and a height of 10 cm. can be put into the formula as V=1/3pi(6)^2(10)=376.99 cubed centimeters.  

Finding volume can be very fun and easy if you know how to use the formulas. It is also very helpful! On a side note it is coming to the end of the semester, how sad? I am truly glad that I took math 105 this fall not only did I learn a lot and really have a better understand of math but I have had the privilege to meet some really interesting people (friends). I will always remember my classmates from math 105, Thank you for such a great semester!

 

Evolution Units

We know that when find the perimeter of something that the units are just centimeters, inches, ect, and when we find the area of something that the units are squared, but what about finding the volume of something. What are the units for this? When finding volume the units are cubed. These can be very hard to remeber, however one way that I remeber is that anything that can be measured with a single string is going to just be units. Painting is how I think of area or surface area, these units are squared. Then for volume I think of 3D figures and know that the units are cubed.

 

 

Area of Shapes!

Finding the area of a square and rectangle are easy to find. The forulma for find the area of a square is 4S, and the forulma for the area of the rectangle is 2W x 2L. These are two basic forulmas that make finding area easy. However when you get into shapes like a triangle and dont know the parts that you need, you can make these shapes in to ones that we know.

When finding the area of a triangle can be difficult if you dont know all the parts or if it is part of another shape. For examlpe if the the triangle is inside a square and we can find the area of the square we can find the area of the triangle. The picture below is a square with a triangle inside it we want to know the area of the triangle.

We know the area of the square by counting the square inside of the big one. The area of this square is 12 square centimeters. After finding the area we can cut out the triangle which we want to find the area. The picture below is cutting out the triangle, notice that when you cut out the one triangle the two extra parts make the same triangle.

With two triangles that are the same, we can conclude that the area of one triangle is half the area of the square. The area of the trangle is 6 square centimeters. The formula for the area of a triangle is 1/2BxH. We can also use this to find other shapes that we do not know. If the shape can be made in to a square or a rectangle this is a good way to find the area of something!

 

Shapes in circles?

Have you even been told to draw a shape in side a circle and not know what they are talking about? Well it is very possible to do, you can do this by taking the central angle of the circle divided by the number of side the shape will have. For example a circle has 360 degrees and a regular hexagon has 6 sides; we would take 360/6= 60, each angle from the center of the circle would then be 60 degrees.

Next we can connect the verticies, creating the six side of the hexagon.

Now that we have our hexagon, another thing that we can find is an angle of the hexagon, we can find the vertex angle by taking 180-the central angle, in this case 180-60=120 degrees.

We can put any shape inside a circle. All you have to do is follow the steps, not only is it interesting but is also fun and can be made into different types of projects!

 

Feet to Centimeters….

In Math we can be given a problem in one unit and have to give the answer in another. This is called converting of units. We can go from feet to centimeters in a few easy step when knowing the converstions.

The Conversion units for Length are:

English                   Metric                            Bridges

12in=1ft               1km=1000m                    1in=2.54cm

3ft=1yd                1m=1000mm                   1mi=1.609

5280ft=1mi          1m=100cm         

                            1cm=10mm

We need the bridges to be able to go from metric to english and viscera. There are also other conversions that can be helpful; Conversions for mass and time.

The Conversion units for Mass are:

English                  Metric                   Bridges

16oz=1lb              1000mg=1g         454g=1lb

2000lb=1tons       1000g=1kg           1kg=2.2Lb

The Conversion units for Time are:

60 sec=1 min    52 wk= 1 yr

60 min=1 hr      365 days=1 yr

24 hr= 1 day     10 yr= 1 decade

7 days= 1 wk    100 yr= 1 century

With these conversions units we can do conversions. We can take 2.6 meters and convert it to millimeters. We can do this by starting with 2.6 meters and finding a conversions that will take use to millimeters.

We can also convert 3.0 miles into inches.

 

Irrational Numbers

A rational number is a number that can be written as a ratio; which means it can be written as a fraction. 10 is a rational number because it can be written as 10/1. Any number that is not rational is considered an irrational number. An irrational number can be written as a decimal; however not a fraction. Irrational numbers also have a decimal that is not ending but it is not repeated. An example of an irrational number is pi. Pi is equal to 3.141592…….., another example is square root 2. Even though square root 2 is an irrational number, this doesn’t mean that all roots are irrational numbers.

We can also simplify roots with a higher index. An index is a number written in the “check mark” area of the radical, that indicates some other root besides a square root.

When we simplify we need to pay attention to the index. The Index is important when simplifing because that is the number of grouping that you need to take out.

We need to find groups of three when simplifying. We can simplify 162 by using a factor tree.

Then we can rewrite this under the ratical.

Pulling out the group of three and taking it to the front of the ratical leaving the 3*2 underneith the ratical.

Then we can simplify the 3*2 under the ratical.

 

Out of 100!

Finding a percent can be very intimidating, however if with start with an easy percent to find we can build off that. A percent that is easy to find is 10%, you just move the decimal one place to the left. For example 10% of 52 is 5.2, we also know that 10% of 6.3 is 0.6. Not only can we find 10% of a number but we can find 20 percent. To find 20 percent of a number we can find 10% and the double it. For example if we want to find 20%of 600, we can first find 10 percent which is 60 and then double that to 120, so 20% of 600 is 120.

We can also use this for finding the new price of an item, for example if we had an item that is $200 and you get 20% off what is the new price? You can start this problem off by finding 10% of 200 which is 20 and then doubling 20 to get 40. The new problem is $40 off $200 so you will pay $160 for the item.

We can also use these methods to find a smaller percent like 5, because 5 is half of 10 we can find 10% of a number and then split it in half. For example 5% of 4200. We can start this problem by finding 10 percent; 10% of 4200 is 420. Then we can take half of 420 and get 210. So 5% of 4200 is 210.

Another way to find a percent is to use a percent chart. Below are to images of percent charts.

These grids have a hundred squares to represent 100%.  The problem for the first grid is 40% of 200. Which is 80.

The problem for the second grid is 20%of 40. Which is 8.