Norien's Surface Area and Volume Post

Rectangular Prism
Shape/ Net:

Solution:
To find the total surface area (TSA) of a rectangular prism, the first step is to find the areas of the six faces of a rectangular prism. To find the areas, you have to find the lxw of the top, front, and side to get the area of one face. 5x10= 50 m² (Top), 6x10= 60m² (Front), and 6x5= 30m² . Once you have the lxw of the top, front, and side of the faces, you add it all up and get 140. With the 140 you multiply it by two to get all six faces of the rectangular prism and the answer to the total surface area would be 280 m ²

lxw

5x10 = 50 m ²

6x10 = 60 m ²

6 x 5 = 30 m ²

TSA = 2(T+F+S)

= 2(50+60+30)

= 2(140)

= 280 m ²

Triangular Prism

Shape/ Net:

Solution:

To find the total surface area (TSA) of a triangular prism, the first step is to find the areas of the three faces of the rectangles in a triangular prism. You have to multiply the length and width. To find the length you have two choices, you can either multiply it one by one like, 10x5, 9x5, and 8x5 or you can add the 10cm, 9cm, and 8cm and multiply it by the width which would both equal to 135cm ² . After finding the area of the rectangle faces, you have to find the triangle faces. To find the rectangular faces, you have to use the formula, which is to multiply the base by the height and divide it by two. 8x9 = 72, 72/2 = 36 cm² . After you find all those areas you add them all together (NOTE: Don't forget to add another 36 because there are 2 triangles in a triangular prism), the answer would be 207cm ²

lxw

= 27x5

= 135 cm ²

= 36 cm ²

= 36 cm ²

^-----------

²⁰⁷cm ²

bxh

--------

2

8x9

--------

2

72

------

2

= 36 cm ²

Cylinder

Shape/ Net:

Solution:

To find the total surface area (TSA) of a cylinder, the first step is to find the radius if they give you the diameter, or find the diameter if they give you the radius because you will need both.

In this cylinder they gave us the diameter which means we will need to find the radius and to find that we need to divide the diameter in to two, which would mean we would have to divide 8 by 2 and get 4mm. The next step would be to find the circumference of the rectangle. To find that you will need to use the formula which is c= π d, c= 3.14x8, c= 25.12mm. Next you will multiply the length times the width of the rectangle. The length would be 25.12 and the width be 12 and when you multiply those two together the answer would be 301.44mm ² . Next, you will find the area of the circle and to do that you use the formula; a= π r, a= 3.14x4, a= 3.14x16, a= 50.24mm ² . Lastly, you have to add the area of the rectangle (301.44) and the two circles (50.24) together which would get you, 401.92mm ²

^{If you did not understand my explanation or need more examples, here is a link.}

Volume

Volume of Rectangular Prism
To find the volume of a rectangular prism, you have to multiply the length, width, and height together. Remember: It doesn't matter which one you multiply first because technically they will all equal to the same number, no matter the order.

v= l x w x h

v= 16 x 20 x 8

v= 2560 cm ³

Triangular Prism
To find the volume of a triangular prism, you have to multiply the base and height and divide it by 2, to get the area of the triangle. Then you have to multiply the second height (non- triangle number) by the answer to the area of the triangle.

v= (b x h1 / 2) x h2

v= (3 x 5 / 2) x 8.5

v= (15 / 2) x 8.5

v= 7.5 x 8.5

v= 63.75 m ³

Cylinder

To find the volume of a cylinder, you have to use the formula, π r ²h. First, you have to find the radius by dividing the diameter by 2. Then you have to square the radius and then multiply the 3.14 by the answer you got

for the radius and then multiply it by the height of the cylinder.

r= d/2

r= 12/2

r= 6cm

v= π r ²h

v= 3.14 x 6 ² x 15

v= 3.14 x 36 x 15

v= 1695.6 cm ³

How To Get the Volume of a Fraction of a Triangular Prism

To get the volume of a triangular prism is already on my post (second one). But What isn't on mine is how to get a fraction of a triangular prism. First you have to divide the numerator by the denominator and the decimal you get from that, you have to multiply it by the answer you got from the triangular prism volume.

v= (bxh1/ 2) x h2

v= (4x8/ 2) x 6.5

v= (16/ 2) x 6.5

v= 8 x 6.5

v= 52cm ³

^{fraction : 3/ 8 = 0.375}

^{0.375 x 52 = 19.5} cm ³

Homework Book Pg. 28 - 29 ( 3, 5, 7)

3. To find these answers, you have to find the two closest square roots that has 5, 18, 78, or 95 between. (depends what question you are doing)

5. a) calculated answer : 4.123 (rounded to the nearest thousandths)

b) calculated answer : 9.219 (rounded to the nearest thousandths)

(first way) You have to find the two closest square roots to the number you are looking for (17 & 85) and then determine whether it is less than half way or more than half way. After you figure that out, you put a decimal either less than .5, more than .5, or exactly .5

(second way) You have to find the two closest square roots to the number you are looking for (17 & 18) and subtract the larger square root to the smaller square root and that will be your denominator. Your numerator will depend on how far your number is to the smallest square root. Eg. 17 is one away from 16 therefore the numerator will be 1.

7. To answer this question, I did almost the same thing as number 5, except I changed the numbers.

Here is a video about estimating square roots. It isn't really how we learned it today but it's almost the same, just a different way.

Here is a link to help you with estimating square roots. It really helps! (:

1. Answer in a short paragraph and with diagrams.

The a² and b² represents the area of the two legs and the c² represents the area of the hypotenuse which is also the longest side of a right triangle. The pythagorean relationship determines whether or not the triangle is a right triangle by adding up the two areas of the legs and if a² + b² = c² it is a right triangle. If a² + b² do not add up to c² it is not a right triangle.

2. Solve for the missing side length.

3. Is this a right triangle? Prove it!!!

No, because the sum of the area of the two legs do not equal to the hypotenuse. In conclusion, this triangle is NOT a right triangle.

Norien's Homework Booklet Scribe Post (5, 7, 8)

5. The commision for the sale of a house was 6 3/4% (6.75%). If the house sold for $345 000, how much was your commision ?

I started off with 100 and then divided it by 10, which I divided by 2 to get the '5' for the 6.75%. After that, I went back to the 100 and divided it by 100 to get 1, which I would later add to the 5 I got before. Then, I divided 1 by 0.1 and then divided the 0.1 by 7.5 to get 0.75 which is the same as 3/4. I got 0.75 by dividing 3 by 4. After I got all the information I needed, I added the 5, 1, and 0.75 which would all add up to 6.75 or 6 3/4. For the "$" side, I used the same method and added the numbers up and got 23 287.5 or $23 287.50 .

7. Estimate the following answers, then calculate. Show your thinking.

a) Miguel bought a car for $4700. He made a down payment of 19 1/2% (19.5%). How much was the down payment ?

I estimated the 19.5% to 20% and the $4700 to $5000. I started off with 100 and divided it by 5 and got 20. Then I went to the "$" side and divided 5000 by 5 too, and got 1000.

b) About 5.6% of Canadians have Type 2 diabetes. If Canada's population is 32 million, about how many Canadians have this condition ?

I estimated the 5.6% to 5% and the 32 000 000 to 30 000 000. I started off with 100 and divided it by 20 to get 5. Then I went to the "population" side and divided it be 20 too and got 1 500 000.

c) The 4900- seat hockey arena was 63% full. How many people were at the game ?

I estimated the 63% to 60% and the 4900 to 5000. I started off with 100 and divided it by 5 and got 20, which I multiplied by 3 to get 6. Then I went to the "seats" side and divided 5000 by 5 to get 1000, then I multiplied that by 3 and got 3000.

*There can be other possible estimations

8. The Nile River is about 209% the length of the Yukon River. If the Yukon River is 3168 km, how long is the Nile River (to the nearest km) ? Show your work.

I started off with 100 and multiplied it by 2 to get 200 for the 209 %. Then I divided 100 by 100 to get 1, which I multiplied by 9 to get 9 for the 209%. On the other side (km) I did the same thing and then added 6336 and 285.12 together and I got 6621.12 km, but the question said to round it to the nearest km. So, since the number after the decimal is a 1, I don't make the number higher therefore keeping it the same. So the answer is 6621 km.

Here is a video that will hopefully help you with finding percents.

Here is a LINK to a "finding a percent" game. Enjoy ! (:

Norien's Graphing Post

1) Bar Graphs - Advantage : It is best for comparing data across categories.
- Disadvantage : Depending on the scale, it is difficult to determine the actual
number.

Double Bar Graph - Advantage : It is best for comparing two sets of data across categories.
- Disadvantage : Depending on the scale, it is hard to know the exact number.

Circle Graph - Advantage : It is best for comparing categories to the whole using percents.

- Disadvantage : You have to change the number into a percent. If the number isn't a percent.

Pictograph - Advantage : It is best for comparing data that can be easily counted and represented using symbols.

- Disadvantage : It is difficult to use the pictograph for data that is even or easy to multiply and divide.

Line Graph - Advantage : It is best for showing changes in data over time.

Disadvantage : This type of graph can only be used for data the change over time and it is hard to identify the exact number, depending on the scale.

2) How can graphs be misleading. Show 3 ways.

• Distorting the scale

• Distorting visuals

• Distorting the bar size

3) a) The following chart shows Pizza Sub Sales over a month. What 2 graphs would show the information accurately?

• Bar Graph

• Line Graph

3) b) If you were selling Pizza Subs would you continue? How does your graph explain your answer.

Yes, I would continue because the sales of pizza are going higher each week and not the other way around, as seen in my two graphs.

4) If you had to convince Mrs Mota that we should continue selling healthy choices which graph would you choose? I would show Mrs. Mota the line graph because you can see the data clearly and how much it has been growing for 3 months. And because you don't have to multiply, like you have to in the pictograph, to see the exact amount.

4) a)

Graph paper : http://www.core77.com/hack2school/img/cs_graphpaper.jpg

Norien's Pay it Forward

Part 1

What is "Pay it Forward" ?

Pay it Forward is a movie that the grade 8 students had to watch. The movie was about a guy named Trevor and how he wanted to make a difference. It all started when his teacher talked about it in the first day of school. Trevor's idea, to make a difference, was to perform an act of kindness for three people, but it has to be something that those three people cannot do on their own. When the person/people ask what they can do to pay you back, you say, "You have to pay it forward." Which means that he/she will have to perform an act of kindness to three other people and the three other people have to perform an act of kindness to three other people, and so on. Which will create a kind of domino action and soon a lot of people will be making a difference. The main idea is, that one person can make a difference even if your act of changing the world isn't that big, you'll still make people happy or help them in a way and, to them you have made a difference.

Part 2

What was your Pay It Forward act of kindness?

Why did you choose this activity?

Who did you help?

What did you do?

When did you do your act of kindness?

Our act of kindness was to give treats to the children tin the Children's Hospital. I chose to this activity because I really like children and I felt sad for the children that have to stay in the hospital and can't go outside or school to play with their friends. Sometimes, I feel guilty because I have a healthy life and at times, I don't appreciate it enough, that's why I wanted to give children that are sick some toys to play with, although it isn't much, I hope I/we made them happy and forget about their sickness, even just for awhile. My friends, Nicole, Nikka, Beverly, and I helped and hopefully made some children in the Children's Hospital happy. On November 10, after school, I bought cookies in Superstore and then went to dollarama to buy toys, like Play-Doh, stickers, stamps, and more. After we bought the treats, three days after, we went to the Children's Hospital Foundation to give them. We weren't able to meet with the children, although, the workers there were really nice and they said that they would give them to the children, and that they were very thankful. After we went to the Children's Hospital Foundation, we had some extra time before my dad would pick us up so we went to St. Agnes Guild Gift Shop, in the hospital, and we bought stuffed animals. The lady that worked there told us that the money we spent on the stuffed animals will go to the Children's Hospital of Winnipeg Research Foundation, which surprised me, but at the same time I felt happy to be donating some money, without even knowing in the first place. We went to the Children's Hospital Foundation on November 14, at lunch.

If we can make a difference, you can too. (:

I hope you like it.

Part 3

How did your act of kindness go?

What Happened?

How did you feel?

How did the person or people react?

Did you ask the person or people to "Pay It Forward"?

How did they react to your request?

If you did not ask the person to "Pay It Forward" how come?

I felt like my act of kindness went very well because when we gave our treats to the workers there and told them about our project, they were very happy and looked really fascinated of what we were doing. Although I didn't see any of the kids reactions I felt really good that we helped and I was really happy that everything we planned, went smoothly. We couldn't ask the children to "Pay it Forward" and we didn't know if we should ask the workers to "Pay it Forward" because we didn't really do anything for them, but we gave them the yellow sheet of paper that explains what "Pay it Forward" is and even talked to them about it for awhile. Although we didn't ask them anything, I think they got what we were trying to do and maybe they might even "Pay it Forward."

Part 4

Why is the idea of "Pay it Forward" important?

Has your act of kindness made a difference?

In my opinion, the idea of "Pay it Forward" is really important because if this alone can make the world a better place in different ways, imagine what other ideas can do. To "Pay it Forward" you don't have to do that much and there's various possibilities, it could be endless if you think about it and in the end you'll still make someone happy and maybe even forget about their problems. I also like how the person you help doesn't have to do anything back for you for your act of kindness instead they do an act of kindness to someone else. In some ways, this idea of "Pay it Forward" can really make you a better person and it will teach you to be less selfish and think of others, even for just a little while. This idea will be a good inspiration for others and maybe even children, because "I believe the children are our future." In my opinion, I think my act of kindness made a difference because, seeing the expressions of the workers in the Children's Hospital Foundation, made me think, "if the workers are this happy, imagine the children's faces." I really hope we made a difference to them. Because of this project, it made me want to help more people, not because of school or a project, but because of the feeling I get when I help people. I feel mushy inside, but at the same time I feel overly happy that I helped someone. (:

Norien's Proportion Post

TASK ONE

Ratio - It is a comparison of quantities that have the same units.

Rate - A comparison of 2 quantities measured in different units.

Proportion - An equation that states two ratios (fractions) are equivalent.

TASK TWO

1. 5 hours to travel 360 miles is about _____ mph.

hours 5 (÷5) 1

-------- -------- = --------

miles 360 (÷5) 72mph

2. As a playgroup worker,if I increase the amount of apple juice I am serving at the playgroup from 25 ml to 100 ml, how much should I increase the the orange juice to, to keep the quantities in the same proportion? The orange juice is 50 ml to start with.

apple juice 25ml x4 100ml

----------------- -------- = ---------

orange juice 50ml x4 200ml

TASK THREE

What are three ways you canprove that equivalent ratio statements are true ?

3/4 = 12/16

TASK FOUR

TASK FIVE

http://www.concurringopinions.com/wp-content/uploads/2011/10/CrimeInAmerica2.jpg

1. Does this seem fair ?. In my opinion, I do not it is fair.

2. With what you know about proportion look and read what is in the image above. Does it seem just and fair ? Why have you made this choice ?

I think that this does not seem just or fair in any way at all because Paul R. Allen only got a 40 months (3 years) sentence in jail for steeling 3 BILLION dollars, while a homeless man stole $100 bill from a bank and got a 15 years sentence in jail even though he turned himself in, after realizing what he did was wrong but he only did that because he actually needed some money. Paul R. Allen stole way more than half of what Roy Brown stole and he got sentenced to less than half of what the judge sentenced Paul R. Allen, which I find racist and revolting in so many ways.

3. What would you have done if you were the judge ?

I would've put Paul R. Allen to jail for 15 years instead of Roy Brown, maybe even twice as long or more. Because for steeling that much money is just unforgivable and what would he have done with that much money anyway ?! For Roy Brown's time in jail, I would've decided for about 40 months (3 years) or less since he turned himself in and didn't take all the money the teller gave him. In this case, he actually needed the money and not just to spend it on his own pleasure but o he could put a roof under his head.