**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.**

** 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...

ReplyDeleteThis is what I did from top to bottom:

ReplyDelete1. 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.

Michelle I think Jeric might be onto something.

ReplyDelete