Question

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

Answer 1

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?

Answer 2

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 ....

Answer 3

it's not a cylinder!

its like a lampshade kinda thing - two semicircular shades, and a rectangular background.

Answer 4

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

Answer 5

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

Answer 6

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?

Answer 7

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

Answer 8

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..

Answer 9

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

Answer 10

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

Answer 11

113 + 168 isn't right?

Answer 12

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

Answer 13

what are your options?

Answer 14

78π in2 84π in2 108π in2 120π in2

Answer 15

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.

Answer 16

I got one answer :D

Answer 17

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

Answer 18

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

Answer 19

First find the area of two semicircles

area of semicircle = (pi * r^2)/2
=pi*(6)^2/2 =18pi

2 semicircles =18pi+18pi=36pi

Answer 20

did you understand til this ?

Answer 21

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

Answer 22

Now its half of a cylinder

Answer 23

and i guess the rectangular part is open

Answer 24

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?

Answer 25

@cbrusoe ??

Answer 26

yeahh i can do it thank-you =)

Answer 27

can you tell me the lateral surface area of it ?

Answer 28

take your time np

Answer 29

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

Answer 30

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

Answer 31

so what will be the lateral surface area ?

Answer 32

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

Answer 33

Yes this is the lateral surface area of a cylinder but we have only half of a cylinder

so divide it by 2

Answer 34

and add the area of 2 semicircles

Answer 35

ok so 84 plus the are of 2 semicircles

Answer 36

Yes

Answer 37

so what is it ?

Answer 38

120

Answer 39

i may have calcuulated that last part wrong