pyramids and cones :)

Aim: How do we find the volume of pyramids and cones?
By using the appropriate formulas.

What is a pyramid?

A pyramid is a polyhedgron that has a polygon as a base and all line segments connect
to one point called the apex.



Hint: when you are finding the volume it is always in cubic meters.

The formula for the volume of a pyramid is the following:


The area of the base times the height divided by three  equals to the volume of a pyramid.
In order to find the area of the base you need to follow the the following formula
A=1/2nas which is the number of sides times the apothem times the number
 of sides divided by two.
Here is an example:



Try it on your own:

What is the volume?


Cones
A cone is a solid figure that has a circle as a base and connects to a point called the vertex.


How do you find the volume of a cone ?

The formula is

Here is an example:
Radius = 2 cm

 
Try it on your own!

Cone with radius of 300 meters,what will be the volume?

 

 

 

Aim: How do we find the surface area and volume of a sphere?

By using the right formula you can find the surface area and volume.

First of all what is a sphere?

A sphere is a three demensional solid that has infinity radiis that all connect to the
 main point which is the center.

It looks like this.


In order to find the surafce area you need to do the following:

S.A.= 4 pi r2
Here is an example

Example 1:  r = 3 ft. Then you just substitute the number in the formula.
SA = 4(π)(3 ft)² = 4(π)(9 ft²) = 36π ft² (in terms of π) or 113.0 ft².

Try it on your own:

A sphere has a radius of 3m what is the surface area?

Focus: how can we identify 3 dimensional Figures?

What is a 3 demensional figure?
A three dimensional figure is a solid that Obtains length, width, and height.

What are some examples of 3-d figures?
Some examples of three demensional figures are spheres, rectangular prisms, cylinders, and a cube.

Sphere- A round solid figure, and every point on it is equidistant from it center.



Rectangular prism - A three demensional solid that has 6 rectangular faces. It is also called
 a cuboid.


Happy b- day  to my nephew again!!

Triangular prism- A three demensional solid figure that has triangles as bases and rectangles as lateral faces.

yum!


Cylinder- A solid three demensional figure which has 2 circles as a base and a rectangles as the lateral face.

CYLINDERS

Aim: How do we calculate surface area of cylinders?

By using the formula  (.-.)!!

What is a cylinder?A cylinder is a solid geometric figure with straight parallel sides and
a circular or oval section.

As you can see a cylinder has two circles as a base, and the round body is actually a rectangle.








How can we solve for he surface area of a cylinder?

Onw way is by calculating the area of the bases which is (r squared times pii), and adding the area of the bases to the area of the rectangle which is length times width.

Example:



The radius is 6 inches. You have to multiply the radius to the square.
Which is 36 inches cubed. Then, multiply times pii,which going to  be 113.09 inches squared.
Then, you add that to the area of the rectangle which is 300 inches squared because the height is 25 inches and the diameter gives you the width which is 12 inches because the diameter is twice the rdaius and the radius is 6 inches so 6 * 2  equals twelve. Finally, you add 300 inches squared with 113.09 squared, which gives you 413.09 inches cubed.

What is the formula?

The formula for the surface area is the following:



All you have to do is substitue the number with radius and you will get the surface area-.-

Example: The radius of a circle is equal to 7. And height equals to 15

SA= 2pii r squared + 2 pii r h.
SA=2 pii 7 squared +2 pii 7 *15
SA= 2 pii 49 +2 pii *105
SA= 98 pii + 210 pii
SA= 308 pii
SA= 967.61


                                                Try it on your own!!


What is the surface area for the given cylinder??


ALL PICTURES FROM GOOGLE.

Aim: How do we solve compound area problems?

You need to find the area of the first figure and add the sum to the area of the second figure.

Example:



As you can see this figure can be divided into two rectangles. First step you divide the figure in to two figure or more if needed.
In this figure, we have two rectangles. To find the area of a rectangle you need to multiply the length and the width.
For the rectangle on the left side, the height is 9 cm. We need to find the width. As you can see on the top of the rectangle on the right there is a measurement of 6 cm. On the base there is a mesurement of 10 cm . You subtract 10 -6 which gives you . The next step is that if we cut the rectangle all the way from the 6 cm lines the height will not be 9 cm. On the right side there is a line that says 2 cm you have to subtract 9 from 2 which will give you seven.
Then, you multiply 4*7 which will give you a product of 28cm cubed.

For the second rectangle, we already got the measurements for it the width is 2cm and the length is 10 cm. 10cm * 2 cm equals to 20 cm squared.
Lastly you add the areas of the two figure and you are left with 28 cm cubed plus 20 cm cubed and you get a sum of 48 cm cubed, and that is your area.



                                                   Try it on your own!!


What is the area of this figure?




All info. from my brain and pics. from google.com.

Aim: How do we find the area of circles?

You can find areas of circles by using the formula which is going to be tought through this lesson.:)

Circle
What is the formula for the area of a circle?



Pii times the radius to the cube(square).

 Here is an exapmle:

A circle has a radius of 22. First you are going to ssquare the radius which will give you 484!!
After that you multiply by pii. Then you multiply by pii. You`re final product is 1,520.53.


What about if they give you the diameter and not the radius?
All you need to do is divide the diameter by 2 since the diameter is twice the size of the radius.


Here is an example,



You divide 38 cm by 2. Which will give you 19.
Then, you multiply by pii. Which will then give you a product of 59.69.

How about if they give you the circumference?
 First of all in order to find the circumference of a circle you need to multiply diameter times pii.
In order to find the area of a circle you need the radius. Therefore, you divide the product by two and you will get the radius. From there, you move on and multiply by pii.

Here is an example:



This circle has a diameter of 18 and when you multiply by pii you get 14.85. You divide the diameter by two which gives you 9. Nine cubed equals to 81. Then you multiply by pii and you get a product of 254.46.


                                                 Try it on your own!!

What is the area of of a circle which has a radius of 234 cm? Hmmmmmm?

All info. from my brain and pics. from google.com

Aim: How do we find the areas of parallelograms,kites, and trapezoids?

By using their formulas.

Parallelograms

How can we find the area of a parallelogram?

Well, one easy way is by using the formula.

The formula for a parallelogram is the same formula for a rectangle!!!!

Because if slice out one of the slanted edges of the parallelogram and put it togeether with the other side you get arectangle.

 Equals to area of


Recall: What was the formula for rectangles?
Base *hieght = Area

So if the parallelogram has a height of 7.6 in. and a base of 6in. the area is
going to be 45.6 cm cubed.

Try it on your own!!

What is the area of the parallelogram below?



Kites


\

Just follow these steps identify the d1  and d2.




Try it on your own!!



Trapezoids

A trapezoid is a quadrilateral with on pair of parallel lines.

The formula for a trapezoid is the following;



AB =base 1 DC = base 2.

Area= height*base 1 + base2 / 2.


Try it on your own!!




What is the area of the figure above?

All info. from my brain and  images from goolgle.com