What Are Cones and What’s The Volume Of A Cone?
There are a lot of common space figures that are well known. Some of these space figures can be considered as polyhedra but some like spheres, cylinders and cones are not polyhedra because they have curved surfaces as opposed to the flat surfaces of the polyhedra.
Right now, let us focus more on the cone. A cone is known to be somewhat similar to a triangle in terms of shape but it has a circular base. The vertex is also the one on top and it may or may not be directly on the center of the base. If you have an ice cream cone at home, it will be like placing the ice cream cone upside down. This three-dimensional geometric shape may have a flat base or a circular base depending on what type of cone it is. Cones can have different volume results depending on their base area. Some say that a cone is highly similar to a pyramid but instead of having a square base, the base is more flat or circular.
The formula for the cone volume is V= 1/3 Bh. This is usually the first formula that you have to know but if you want a more complex formula in order to find out the volume of a cone, you need to substitute the (Bh) with the formula for a circle. The formula for a circle is πr2 so you can easily say now that to find the cone volume you need to use the formula V = hπr2/3.
You may be wondering now what is the main purpose of figuring out the cone volume ? Volume in general allows you to know the amount of space that any solid figure occupies. This means that if you would like to measure how much space is occupied by a huge cone, you need to know its measurements to figure out its main volume.
In detail, here is the process that you can follow so that you can easily find the volume of the cone. The first step that you have to make is to look for the radius. In order to know the radius, you need to know the diameter of the cone and divide it by two. Now that you know the radius, you need to use it in order to find the area of the circle. The formula for this is A=πr2. First of all, change r to.5 then, you need to square the radius and multiply that with the value of π. This process can help you get to know the cone volume.
Once you already have the area of the circle, you need to know the height of the cone in general. This is not needed anymore if the height of the cone is given but if not, you may need to measure it with the use of your ruler. You need to multiply the base of the cone with the height of the cone then divide the product by 3.
There are some things that you have to remember when you are trying to find out the cone volume. First of all, you need to make sure that you have all the right given measurements. If this is for a test and all the measurements are given then you just need to memorize the formula in order to figure out the right answer. You also need to make sure that you know all the right units of measurements to use. Some professors will mark your answer wrong if you use the wrong units. Be wary of this so that you can be sure about what you will get.
It is important to take note that there may be various details that would have to be considered when it comes to figuring out the cone volume. Some of the other types of cones are the following:
- Right Circular Cone (V=πr2 h/3). This is the type of cone wherein the base of the cone is circular. The formula for the volume of the cone is mentioned above. Right Cone is the typical type of cone wherein the vertex is placed directly on top of the cone. The base of the cone is not circular and is usually flat. Oblique Cone is the type of cone wherein the vertex is not directly on top of the center of the cone. The base of the cone may be flat.
There are other types of cones that may arise depending on the circumstance such as the Inscribed Cone and the Circumscribed Cone. The formula of inscribed cone and circumscribed cone can be different depending on the figures and the circumstances that will be given. There are still other types of cones that may arise and the cone volume may be different each time.
The Cone in Modern Life
It seems that there are a lot of people who do not realize how they make use of the cone volume in real life. Of course, knowing the actual measurements can be hard to implement but when you look all around you, you will see a lot of cone shaped objects. The cone can be as easy to see as the shape of the ice placed on a snow cone or it may also be in other forms like funnels.
For students who are also studying science, the funnel is one of the items normally used in the lab that is shaped like a cone. Sometimes, you would need to figure out the volume of the water or other liquids that you are passing through the funnel so as to easily understand the volume of the cone.
When it comes to nature and surroundings, the various mountains seem to be in the shape of a cone. They usually have circular bases and there are some that may be more perfect than others. For those who are highly interested to know the height and base of these mountains, knowing the accurate formulas for figuring out the measurements of the mountains are important. Does a case study have to be done in order to actually realize the different cone-shaped items that can be found in the world right now? Perhaps being more observant can help people become more aware of what they see in this world.
There are also instances when the small things that you use in your life are cone shaped. Have you ever realized that the shape of the cover of your pen is similar to that of a cone? What about the traffic cones that you shouldn’t hit when you are doing your driving exam? Those are in the shape of cones too. It is all about realizing the number of cone-shaped items that you actually see at the present time to realize why the cone should be given importance too. It is not surprising though that it is not really considered to be as one of the people’s favorite shapes. Kids will probably not recognize the cone as a shape as they are more inclined to know more basic shapes. It is only later on that they will realize the importance of the cone volume.
It has been said that since the time of the Sumerians, the cone has already been used as a part of their counting system. They have created clay stones that are in the shape of a cone in order to signify “one.” They have also used other shapes in order to signify other numbers. For instance, they used a clay ball to signify ten and they also used a larger shaped cone to signify 60. At that time, most of the numbers were only counted up to 60 mainly because this number has a lot of divisors. 60 is the only integer divisible by 1,2,3,4,5 and 6. The Babylonians were the ones who created a circular figure to signify zero. Truly, the cone has gone a long way. However, the cone volume may not be tackled yet at that time.
Back to how cones are being taught to children at the present time, kids are learning about cones earlier than before. It will be up to the teachers to explain how the concept is going to be. It will take a bit of creativity to help children understand what the cone can be used for aside from ice cream. The main reason why math is rarely understood by children is because they become bored with the concept of it. They become bored with the fact that they just have to deal with numbers without realizing that it can actually be easy when these numbers can be used in examples that they can visualize. With math, there is no in between. It is either your answer is right or wrong.
Solving math problems does not require a college paper writing service anymore, as you are not required to write a whole lot of things about something that you have to research about. Some people who do math simply memorize the formula without understanding its concept. This may not be too useful – though this could come in handy for emergencies – because how can math be appreciated without knowing the story behind each shape, each item that is being measured, and the origination of the formula? Perhaps an analytical essaymay be better because at least, students would need to analyze and be critical of the things that they have to write about. Sometimes, students are required to make essays like this – that are related to math – such as how they can use the formula of cylinders in their everyday life. Students cannot just search online for the answer. To know the cone volume, they still need to solve. They truly need to analyze how they can actually use the formulas in real life.
There are no clear answers on who created the formula to get the cone volume but one thing is for sure, the formula has done a lot of wonders to people who love mathematics at the present time. There is no serious need for dissertation writing services when it comes to math. All the things that can be focused on are numbers.
It may be fun for some students to get a chance in writing an expository essay so that they can analyze the concept of cones more. Some students would love to feel like they have invented something and this can be explored using an expository essay. Do you think that you have gained enough details about the volume of cones and how you can use it at the present time? Explore the concept more and you will not have any regrets. In conclusion, here are the segments touched thus far:
- What is cone volume and its formula?
- Is the volume of a cone actually important at present time?
- The importance of cone as a shape in everyday life and where they can be seen.
- How Sumerians used the cone in counting
- How writing about the volume of a cone can help in realizing its importance in everyday life.
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