12.4 Volume of Prisms and Cylinders

Hello fellow classmates, and teachers,

If you are unaware, or you were absent, or you didn't read the title, today we learned about volume. Below you will locate a written description and example sheet of volume and a video link. You may choose whichever suits you best. Mr Wilhelm, as you are aware I'm not here in first hour today. Knowing this would you be kind enough to show my classmates the hidden hint and puzzle for them to solve? If you would that would be very sincere, if not, well then I understand. Thanks, and Enjoy.

HINT: CONGRATS!!! After I tried so hard to hide this hint you still managed to process its whereabouts!!! If you would like to "LOSE THE GAME" then you must both read the blog and watch the video. Good Luck!

Volume: measures capacity

Volume: the amount of cubic units taken to fill a 3 dimensional figure

Sorry for any inconvenience, the "blach" was a B, I think the mic on my phone stalled out,

and the vibration noise was my phone ringing. It was the best take I had.

The equation for volume is represented by V=B(h)

With "V" representing volume, "B" representing the total area of the base of the figure, and "h" representing its height.

For example, the formula of a triangular prism: V= [1/2(bh)]H

rectangular prism: V=lwh

Cylinder: V=πr²(H)

and so on...

Blog of the year?

Thank you for reading thy blog post, please subscribe,

I hope you enjoyed everything, for there is a possibility

that this may be my last blog post, (last trimester with Mr. Wilhelm)

Sincerely, Your loyal blogger, cough cough (Peter Kessel),

Oran Lieberman

P.S, the purple letters spell out, I LOST THE GAME.

Law of SINES/COSINES

Fellow Classmates, Mr. Wilhelm, and Stalkers I Don't Know, Friday we learned A. the best way to make your math teacher happy is to hide all of their stuff B. that #A does not apply to Mr. Wilhelm C. #A is actually a letter D. stuff about shapes . . This beautifully color-coded picture illustrates an oblique trigon. Oblique trigons are sad because everyone groans when they see them because their measurements don't do any thing special. "Oh how I wish I could be a SPECIAL triangle!" said a young triangle. One day, Mr. Wilhelm invented a formula for them called THE LAW OF SINES . You plug in an angle (A), the side opposite it (a), and one other piece of information (angle C or side c). You can then solve for the other piece's counterpart (side c or angle C). You (and the triangles) can consider it something of a hero. . . This formula happens to be THE LAW OF SINES don't crowd it . . This is the same triangle from before. Cheap Budget. . . These formulas make up the LAW OF COSINES. The formulas on the left work when you are given SAS. The formulas on the right work when you are given SSS. . . . Here is a website that proves the law of sines Here is a website that proves the law of cosines Here is a website that exemplifies stuff Watch the video about sines and cosines It dosen't work.. but it shows the importance of apologies and good pouty faces Here is an unrelated website . . 'sine' ing off ~~OLIVIA MILLER~~

11.3 & 11.4

Today in class we covered two sections: 11.3 and 11.4.

11.3 was about the area of a trapezoid. To find the area of the trapezoid, use this formula (in this formula, the a and b stand for the base 1 and base 2):





We learned that the formula comes from a few places, such as the ones shown below:

 
You can move the triangles on the sides up to the top of the trapezoid to create a rectangle. 

Here, it shows how the trapezoid the area formula is made. 

• The area of the rectangle is b₁h.
• The area of the triangle on the left side is ½xh.
• The area of the triangle on the right side
  is ½(b₂ – b₁ – x) × h = ½b₂h – ½b₁h – ½xh.
• The combined area of the three pieces, then,
  is b₁h + ½xh + ½b₂h – ½b₁h – ½xh, which simplifies to ½b₁h + ½b₂h. This further simplifies to ½(b₁ + b₂) h, which is the trapezoid area formula. 

(All of this info I found at http://illuminations.nctm.org/LessonDetail.aspx?ID=L580)

Another very helpful website is http://www.mathopenref.com/trapezoidarea.html

On it, you can change the base and the height in an interactive trapezoid. It also clearly explains the formula and has videos you can watch.

Next, we went on to 11.4, which was the area of kites and/or rhombi.
To the area of a kite or a rhombus, you use the formula A= ½ d₁d₂ 
This formula comes from the fact that a rectangle can be drawn around a kite or rhombus and that the kite or the rhombus can be "cut up" and then turned into a rectangle that has an area one half of the big rectangle.

That's about it! I hope that everyone loves our blog at the conference thing. Also, LOST THE GAME :)


-Jessica