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