## cbrusoe 3 years ago 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

1. cbrusoe

2. apoorvk

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?

3. cbrusoe

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 ....

4. apoorvk

it's not a cylinder! its like a lampshade kinda thing - two semicircular shades, and a rectangular background.

5. cbrusoe

i know but if we added the other half... aha ... ok so what equation do i use?

6. apoorvk

find the area of the rectangular part, then are of each semi-circular shade and add em up!

7. cbrusoe

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?

8. cbrusoe

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

9. apoorvk

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..

10. cbrusoe

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

11. cbrusoe

uugh but adding those up gives me to big of a number hmmm

12. apoorvk

113 + 168 isn't right?

13. cbrusoe

well it adds up to 281 which isnt one of my options

14. apoorvk

15. cbrusoe

78π in2 84π in2 108π in2 120π in2

16. apoorvk

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.

18. cbrusoe

it's ok thanks for the help =) and ok =)

19. apoorvk

yeah would be -the last one - just help her understand.

First find the area of two semicircles area of semicircle = (pi * r^2)/2 =pi*(6)^2/2 =18pi 2 semicircles =18pi+18pi=36pi

did you understand til this ?

22. cbrusoe

yeahh when we go to the semi circle stuff i think is when i started to get confused

Now its half of a cylinder

and i guess the rectangular part is open

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?

@cbrusoe ??

27. cbrusoe

yeahh i can do it thank-you =)

can you tell me the lateral surface area of it ?

30. cbrusoe

ok when i calculate 2*pi*r*h i got 263.76

don't take the value of pi .. just keep pi like that since your answer contains pi

so what will be the lateral surface area ?

33. cbrusoe

ok so 2*r*h and my diamiter is 12 so radius would be 6 and height is 14 so 2*6*14 = 168pi?

Yes this is the lateral surface area of a cylinder but we have only half of a cylinder so divide it by 2

and add the area of 2 semicircles

36. cbrusoe

ok so 84 plus the are of 2 semicircles

Yes

so what is it ?

39. cbrusoe

120

40. cbrusoe

i may have calcuulated that last part wrong