Tuesday, October 5, 2010

Michelle's Scribepost for October 5, 2010

Today in math class, we were each given a question to do. My question was number 22. (extend)

22. The plan for a concrete birdbath is shown below. The bowl is a cylinder with a depth of 10cm. If the bowl has a diameter of 30cm, what is the exposed surface area of the birdbath, including the pillar and pedestal?

***** SORRY IF THE PICTURE IS BLURRY.

First I found the birdbaths surface area and circumference (inside and out)
* to find radius, you divide the diameter by 2
Outside: S.A. = 2 π r h + π r ²
= 2 (π x 19 x 15) + π x 19²
= 2 ( 285 π ) + π x 361
= 570 π + 361 π
= 1790.71 + 1134.11
= 2924.82cm

Inside: S.A.= 2 π r h + π r ²
= 2 ( π x 15 x 10 ) + π x 15²
= 2 ( 150 π ) + π x 225
= 300 π + 225 π
= 942.48 + 706.86
= 1649.34cm

Then I found the pillars surface area.
S.A.= 2 π r h
= 2 ( π x 12 x 50 )
= 2 ( 600 π )
= 1200 π
= 3769.91

Next I found the pedestals circumference and surface area.
S.A. = 2 π r h + π r ²
= 2 ( π x 30 x 8 ) + π x 30²
= 2 ( 240 π ) + π 900
= 480 π + 900 π
= 1507.96 + 2827.43
= 4335.39cm

After I had to find the circumference underneath the birdbath and take away the extra area where the pillar goes because it connects.

To find that, you take the circumference of the outside of the birdbath and subtract the circumference of the inside of the birdbath.

1134.11 - 706.86= 427.25cm


FINALLY, you add the exposed parts of the whole birdbath which I think is:

1790.71 (outside of birdbath)
942.48 (inside of birdbath)
427.25 (bottom of birdbath)
+ 3769.91 (pillar)
4335.39 (pedestal)
---------------- < (equal sign)
11265.74cm

I'm sorry, if you don't understand what I did. I tried to explain it as much as I could in words. When I checked my answer in the back it was wrong. I probably did some steps wrong, so just correct me by commenting on my blog. Also I used π instead of 3.14 because it is more "accurate." Since I used that method, I had to round most of my numbers to 2 decimal places.

3 comments:

  1. ** IM SORRY it looks dull, but I actually kind of made it colour coded but it didnt show up on here, it just showed as black...

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  2. This is what I did from top to bottom:
    1. Inside the bird bath:
    a) Surface area inside = πr² = 3.14(15)² = 706.5 cm²
    b) Surface area of the side of the bowl = c(h)
    c = π(d) = 3.14(30) = 94.2 cm,
    Therefore the S.A. = 94.2(10) = 942 cm²

    2. Outside of bird bath:
    a) Top area = big circle - small circle
    Big Circle = πr² = 3.14(19)² = 1133.54 cm²
    Small circle area above = 706.5 cm²
    Therefore the S.A. = 1133.54 cm² - 706.5 cm² = 427.04 cm²
    b) Side = c(h)
    c = π(d) = 3.14(38) = 119.32 cm²
    Therefore = 119.32(15) = 1789.8 cm²


    3. Pilar: c(h)
    c = π(d) = 3.14(24) = 75.36 cm²
    Therefore = c(h) = 75.36(50) = 3768 cm²

    4. Under the bird bath:
    Big Circle from outside (2a) - pilar area (5a)
    1133.54 cm² - 452.16 cm² = 681.38 cm²


    5. Pedestal
    a). S.A. Top of the Pedestal (top area - pilar)
    TOP = πr² = 3.14(30)² = 2826 cm²
    Pillar bottom area = πr² = 3.14(12)² = 452.16 cm²
    Therefore area = 2826 - 452.16 = 2373.84 cm²
    b) Height of the Pedestal = c(h)
    C = π(d) = 3.14(60) = 188.4 cm²
    Therefore S.A. = 188.4(8) = 1507.2 cm²

    The solution to the problem is:
    1a. 706.5 cm²
    1b. 942 cm²
    2a. 427.04 cm²
    2b. 1789.8 cm²
    3. 3768 cm²
    4. 681.38 cm²
    5a. 2373.84 cm²
    5b. 1507.2 cm²
    TOTAL SUM = 12195.76 cm²

    Sorry guys I hope this make sense. I tried to break it down as much as possible. From the answer I'm 6.19 cm² off. It may be because I rounded pi or 3.14.

    Your question is complicated michelle.

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  3. Michelle I think Jeric might be onto something.

    ReplyDelete