## Monday, October 11, 2010

### Michelle's Scribepost for October 8, 2010

Today in math class we learned the difference between visible surface area and total surface area.

Visible surface area is the part of the figure you can see without imagining the back of the imagine.

Total surface area is the whole surface area (all faces) of the figure viewed in 3D.
(Well, thats how I defined it.)

Pink (roof) : S.A.= l x w
= 4 x 7
= 28m²

Yellow (side of house) : S.A.= l x w
= 7 x 2.5
= 17.5m²

Blue (front of house) : S.A.= l x w
= 4.8 x 2.5
= 12m²

Orange (gable) : S.A. = b x h / 2
= 4.8 x 3.2 / 2
= 15.36 / 2
= 7.68m²

Then you add all the surface areas together.
28 + 17.5 + 12 + 7.68 = 65.18m²

After we did that, Mr.Backe gave us a question to solve.
(Here are some things we wrote down before, to help us solve the question)

Word: millimetre centimetre decimetre metre litre gram dekametre hectometre kilometre (American spelling is with the endings "er")
Symbols: mm cm dm (m) (l) (g) dam hm km
Prefix: mi ci di (m) (l) (g) deca(decka) heca kilo
Decimals: 1/1000(0.001), 1/100( 0.01), 1/10(0.1), 1, 10, 100, 1000

If the can is 5dm in height what is its total surface area?
1 cm is 10mm
1 dm is 10cm

First I converted all the units into cm:
36mm/10 = 3.6cm
I used cm since most of the units were cm, so it made sense to pick unit that was mostly used.

Then I found the surface area of the outside of the paint can.
= 3.6 /2
= 1.8

S.A = 2 π r ² + 2 π r h
= 2 π ( 1.8 ) ² + 2 π ( 1.8 ) ( 50 )
= 2 π ( 3.24 ) + 2 π ( 90 )
= 6.48 π + 180 π
= 20.36 + 565.49
= 585.85cm²

Next I found the surface area for the inside of the paint can.
S.A.= 2 π r h
= 2 π ( 1 ) ( 50 )
= 2 π ( 50 )
= 100 π
= 314.16cm²

I didn't find the circumference on the inside of the paint can because the circle part on the inside is gone since there is no lid, and also for the outside of the paint can you still have to take away the circumference of the smaller circle. All together that is two circles that are the same size, so the " 2 π r ² " cancels out.

Sorry if that didn't make sense, but I tried to explain it as best as I could.

Then you add the outside and the inside of the paint can together.
585.85 + 314.16 = 900.01cm²

** SORRY THE COLOURS DIDN'T WORK FOR ME. It kept turning into black whenever I published it.

Thank you for reading my blog, and don't forget to comment. Also correct the mistakes that I may have made, please! The next person I pick to do the blog is JAMIE!