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cbrusoe

Megan bought an outdoor wall light fixture. The fixture has semicircular ends at the top and bottom as shown. The side of the fixture that faces the wall is open. What is the exterior surface area of the light fixture? Answer 78π in2 84π in2 108π in2 120π in2

  • one year ago
  • one year ago

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  1. cbrusoe
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    • one year ago
  2. apoorvk
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    Just need to find the surface area of each semicircle part, and add 'em up. Or rather, two same semicircles make a circle! so, find out the are of a circle which has a diameter of '12in'. Then, add the area of the rectangular part --> 12x14 - right? What do you think now?

    • one year ago
  3. cbrusoe
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    i did something way off ... but im not sure what i found the formula for a cylinder and i plugged in my numbers and calculated it and got 753.6 ....

    • one year ago
  4. apoorvk
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    it's not a cylinder! its like a lampshade kinda thing - two semicircular shades, and a rectangular background.

    • one year ago
  5. cbrusoe
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    i know but if we added the other half... aha ... ok so what equation do i use?

    • one year ago
  6. apoorvk
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    find the area of the rectangular part, then are of each semi-circular shade and add em up!

    • one year ago
  7. cbrusoe
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    ok the area of the rectangular part is 168 now i need to find the area of each semi-circular shade ... how do i do that?

    • one year ago
  8. cbrusoe
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    sorry ive been working since 6 this morning non-stop... i dont think im trying as hard ... cuz this probably something i should get

    • one year ago
  9. apoorvk
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    its okay - i am woozy too :P. area of semi-circle = (1/2) area of circle plus you could think this way - two same semicircles make a circle, so just find the area of the the equivalent circle..

    • one year ago
  10. cbrusoe
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    ok well i know the formula for the area of a circle is pi*r2 so since the diamiter is 12 the radius would be 6 plug that in and i got 113.04

    • one year ago
  11. cbrusoe
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    uugh but adding those up gives me to big of a number hmmm

    • one year ago
  12. apoorvk
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    113 + 168 isn't right?

    • one year ago
  13. cbrusoe
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    well it adds up to 281 which isnt one of my options

    • one year ago
  14. apoorvk
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    what are your options?

    • one year ago
  15. cbrusoe
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    78π in2 84π in2 108π in2 120π in2

    • one year ago
  16. apoorvk
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    i am sorry, it's too late here, and i am too woozy - i misunderstood the whole thing - it must be a cylinder itself - i am really sure this time though. @Diyadiya will help you out. Thanks :) and apologies for misguiding - didn't mean it.

    • one year ago
  17. Diyadiya
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    I got one answer :D

    • one year ago
  18. cbrusoe
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    it's ok thanks for the help =) and ok =)

    • one year ago
  19. apoorvk
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    yeah would be -the last one - just help her understand.

    • one year ago
  20. Diyadiya
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    First find the area of two semicircles area of semicircle = (pi * r^2)/2 =pi*(6)^2/2 =18pi 2 semicircles =18pi+18pi=36pi

    • one year ago
  21. Diyadiya
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    did you understand til this ?

    • one year ago
  22. cbrusoe
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    yeahh when we go to the semi circle stuff i think is when i started to get confused

    • one year ago
  23. Diyadiya
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    Now its half of a cylinder

    • one year ago
  24. Diyadiya
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    and i guess the rectangular part is open

    • one year ago
  25. Diyadiya
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    You just have to find the lateral surface area of half of cylinder ( 2*pi*r*h) half cylinder so lateral surface area = 2*pi*r*h/2 =Pi*r*h can you do it?

    • one year ago
  26. Diyadiya
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    @cbrusoe ??

    • one year ago
  27. cbrusoe
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    yeahh i can do it thank-you =)

    • one year ago
  28. Diyadiya
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    can you tell me the lateral surface area of it ?

    • one year ago
  29. Diyadiya
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    take your time np

    • one year ago
  30. cbrusoe
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    ok when i calculate 2*pi*r*h i got 263.76

    • one year ago
  31. Diyadiya
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    don't take the value of pi .. just keep pi like that since your answer contains pi

    • one year ago
  32. Diyadiya
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    so what will be the lateral surface area ?

    • one year ago
  33. cbrusoe
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    ok so 2*r*h and my diamiter is 12 so radius would be 6 and height is 14 so 2*6*14 = 168pi?

    • one year ago
  34. Diyadiya
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    Yes this is the lateral surface area of a cylinder but we have only half of a cylinder so divide it by 2

    • one year ago
  35. Diyadiya
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    and add the area of 2 semicircles

    • one year ago
  36. cbrusoe
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    ok so 84 plus the are of 2 semicircles

    • one year ago
  37. Diyadiya
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    Yes

    • one year ago
  38. Diyadiya
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    so what is it ?

    • one year ago
  39. cbrusoe
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    120

    • one year ago
  40. cbrusoe
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    i may have calcuulated that last part wrong

    • one year ago
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