Robby's BOB

For the past 2 weeks, we learned how to find surface area's and volumes of 3-dimensional (3D) objects like rectangular prisms and cubes. Here is how to find the Surface area and Volume of a Rectangular Prism:

Surface Area of a Rectangular Prism



This is a Rectangular Prism. You can see the length, width, and height from any angle, meaning it is a meaning it is a 3D object.

Surface area is "how much wrapping you need to cover the whole object". So, if you were to cover it, you much wrapping would you need in a unit of measurement (not squared).







Our new Rectangular Prism has some measurements attached to it, so we can solve the surface area and Volume.


So:
Length = 6 cm
Width = 10 cm
Height = 6 cm

There is 1 formula for finding surface area:

-It is
(Area of L side + Area of R Side) +
(Area of Top) + Area of Bottom) +
(Area of Front + Area of Back)






One important thing must be done to simplify finding the surface area. You must turn the rectangular prism into its 'Net' form, which is as follows:



Now do the equation (Since L side and R side, and Top and bottom, and Front and back have the same area, simply x2 to use less space.:

Surface Area
=(Area of L side x 2) +
(Area of Top x 2) +
(Area of Front x 2)

=(60cm² x 2) + (36cm² x 2)
+ (60cm² x 2)
=(120cm²) + (72cm²) + (120cm²)

=312cm² is the Surface Area





Now Volume is pretty easy, there are 2 different ways on finding it.
One is : Length x Width x Height
the other one is Area of Base x Height

I'll do both to prove they both work:

The measurements are:
L = 6 cm
W = 10 cm
H = 6 cm

The Formula:
= Length x Width x Height
= 6cm x 10 cm x 6 cm
= 60 cm x 6
= 360 cm³ (note, the answer is CUBED or the power of 3 (³) because you are multiplying 3 dimensions together: length, width, and height)




The Second Formula is Area of Base x Height:
Area of Base = L x W or L x H or W x H
Area of Base = L x W (for now)
Area of Base = 6cm x 10cm
Area of Base = 60cm²

Height = 6cm

60cm² x 6 = 360 cm³

See, the answer is 360cm³ for both, meaning they both work.
The Length x Width x Height one is easier, in my opinion, because it takes less work to do.
And that's how you find the volume and surface area of a Rectangular Prism.

Robby's Pythagoras Growing Post

Part 1:
What is a Pythagorean Triple?
-A Pythagorean Triple is 2 square numbers that when added together, equal another square number. The equation for one is:
a² + b² = c²

There are many Pythagorean Triples, but often are confusing to find because when you look at a number squared, like 5², you often ignore or don't see the little ² and end up multiplying by 2 instead of multiplying by 5 again, which is what you should have done. This mistake makes a big difference. 10 is a smaller than 25, and everybody knows that specific math questions have to have an exact answer. A number squared simply means that number times itself. The opposite of squaring is square rooting, which is finding what number times itself equals the larger number.

Anyway, here is my perfect square chart. The highlighted numbers or the ones that are the same color is 1 Pythagorean Triple.














Part 2:

Part 3:

Word Problems:

When reading math related word problems, underline important parts and circle the key numbers. Cross out unnecessary or unimportant information, if there is some:

A pictorial version of this problem would be:


The sides are 90 units because, since the measurements of the sides weren't given, you have to go to common sense for help. A square is 360 degrees, meaning it has 4 right angles (90 x 4 = 360). A triangle is half of a square, so it has 180 degrees (90 x 2 = 180) in angle. But we aren't finding the angle of the sides, but the length. So the degrees sign (°) is replaced with units (or u) in place of a measurement.
The new picture of the problem looks like this:

Now we can simply do the equation a² + b² = c² to solve this:
a² + b² = c²
90²+ 90²= c²
8100+8100=c²
16 200=c²

√16 200 = √c²

127.27= c

So the missing hypotenuse is 127.27 units in length. You have to throw the ball 127.27 units from first base to third base to get throw the runner out.

Part 4:
Create your own problem:

You are racing down the street on your new 10 speed bike. You see a ramp that 2 of your friend are hauling, and you must jump it to prove you aren't a noob. But your stupid friends are hauling it way further than they are supposed to, 3 meters left of you instead of being straight ahead of you. You are 10 meters away now and must swerve to jump the ramp and end up having to jump at an angle. How many meters do you have to swerve to get to that ramp?

Now, with the key parts highlighted:

Now to answer the question:
What we know:
a = 3 meters
b = 10 meters
c = ?

Here's a little doodle I made on how the problem would look.


Now that we have the numbers, we just do the equations and solve it.
a² + b² = c²
3² + 10² = c²
9 + 100 = c²
109 = c²

√109 = √c²
10 9/21 = c

10 9/11 = 10.42
c = 10.42
c²= 109

So, after solving what the missing side was, you now know that you must swerve 10.42 (closest to 10) meters to the left to jump the ramp. Once you do that, and don't break your neighbors car from jumping onto it, you can retire from your career of dare-deviling and get a nice job as a professional lawn mower.

The End (of Part 4 )

Robby's 2nd Growing post

Question 1: 1)What strategies were needed?
-I used a Ratio table, maybe some money strategies, and division and multiplication between both answers
2)How did you use these strategies?
-For the multiplication and division between both answers part, to get 1/2 cups, I answered 12 cups by multiplying 2 2/5 (2.4) by 10 to get 24, then divide it by 2 to get 12. Then I divided 12 by 12 and then by 2 to get 1/2.
( 2.4 x 10 = 24 ÷ 2 = 12 cups 12 ÷ 12 = 1 ÷ 2 = 1/2 cups. *Then do same strategy for the ingredients and price.)
-The ratio table was basically the same information as the multiplication and division part, but with a visual aide and a little neater

3)Or How could you of used these strategies.
-The Money Strategy
-I would have used a money strategy, but it just asked you to find how much it costed, not how many pennies, nickles, and dimes you would need to give Betty to buy her snack mix. So in short, this strategy didn't really help, wouldn't get extra marks for because it didn't answered any questions, and would just be a waste of time.
4)How would you figure out the price of a 6 cup bag of Betty's Snack mix? Use a ratio table
-To get 6 cups, I would multiply the cups and price for a 2 2/4 container by 10, then divide the answer by 2, then divide it by 2 again to get 6 cups.











5)Find 3 other values (amounts of Snack Mix) that could be solved using the same ratio table. Find the $$ of your new container sizes.

-The 3 others are circled in green. For the price of 3 cups, I added the price of a 1 cup and 2 cup container to get it.

Question 2: