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WEB-BASED LESSON: CONES

26 Dec

In our daily life, we are certainly familiar with these following things:

Tumpeng

Rice Cone

hat

Hat

Es Krim

Ice Cream

terompet

Trumpet

Farmer Hat

Farmer Hat

If we look at the objects carefully, we will find that those things have the same shape. Yes, the objects are equally formed one of solid figures with curved surfaces, one of learning materials which have been learned in Elementary School. As we have been learned, solid figures with curved surfaces consists of three types namely cylinder, cone and sphere. What about the things above, are they cylinders, cones or spheres? Look at the objects around us and find the other objects which have the same shape with the objects above!

We can see A Cone as a regular pyramid angular-n with n is approaching infinite. Cone can be formed from a right triangle that is rotated as far as 360 °, where the right side as the center of rotation. Demonstration of cone formation can be seen by clicking the figure below:

Elements of A Cone:

As the above description, a cone is a special pyramid which has a circular base. A cone has 2 sides and 1 rib. The side of the upright cone is not a triangle but in the form of curved cone called a blanket. For a better understanding the elements of a cone, please consider the illustration below:

To learn about the surface area of a cone, let’s start by thinking obout this following problem.

Towards the the new year 2013, Mr. Achmad wants to be a sudden trumpets maker. He plans to make 150 pieces of medium-sized trumpets with radius of 10 centimetres and height of 24 centimetres. If in making the trumpets, Mr Ahmad has a rectangular paper which length and width are 4 ms and 3 ms, respectively. How large is the rest of the paper?

Trumpet_4

Before we help Pak Achmad to determine how large the rest of paper material for the trumpets, let’s watch a video about how to make a cone:

In the video, we have seen how to make a cone. On this problem there is little difference to the case in the video because of the trumpet does not require a base. To determine the area of the rezt of paper material, we must first be aware of how wide the paper is needed to make a trumpet. How to find the surface area of ​​the cone can be studied by using the following applet.

Here is an example on solving the problem of how to find the surface area of ​​the cone.

Once we know about how to find the surface area of ​​the cone, then we can solve the problem by these following Polya steps

polya steps

Thus, the wide of the rest of Pak Achmad’s paper is…

Volume Kerucut:

To learn about the volume of a cone, let’s start with by consider this following problem.

Amounts of ice cream is pouring in a cone-shaped contained with a diameter of 5 centimetres and e height of 15 centimetres. Thus, the volume of ice cream in the container is…

candies5

candies9candies34

To solve this problem, because the shape of ice cream container is cone, then we must know how to find the volume of a cone. As already known, the cone is a pyramid that has special properties in which it has a circular base. The following video is remaind us about the relationship of volume of pyramids volume and volume of prisms which have the same base size.

And this following video explains the relationship about volume of cylinders and volume of cones.

Hence, from those two videos, we can conclude that:

volume

Here is an example on solving the problem of how to find the volume of ​​the cone.

From the explanation above, like the problem of the surface area of ​​a cone, we can use Polya steps to solve this problem. Thus, the volume of ice cream in the container is …

Exercises:

As an exercise, students can utilize learning resources which provide many online questions and problems at the link below:

  1. Exercises on surface area of a cone
  2. Exercises on volume of a cone
  3. Application exercises related to volume of a cylinder and volume of a cone on the link of this following figure

This topic is a part of Solid Figures with Curved Surfaces Material. The complete powerpoint about Solid Figures with Curved Surfaces can be downloaded here.

 
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Posted by on December 26, 2012 in Math Exercises

 

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