Question

HELP!
~MEDAL REWARD~
What is the surface area of the figure?

A.
428 ft2

B.
560 ft2

C.
632 ft2

D.
888 ft2

http://static.k12.com/calms_media/media/1422500_1423000/1422985/1/319d88c1b12d98a6afa5e92521264dc25a2b6dfc/MS_PA_131002_171344.jpg

Answer 1

http://static.k12.com/calms_media/media/1422500_1423000/1422985/1/319d88c1b12d98a6afa5e92521264dc25a2b6dfc/MS_PA_131002_171344.jpg

Answer 2

We can cut it into 2 shapes, a cube with a side length of 6, and a rectangular prism with a length of 14, width of 6, and height of 8.

Answer 3

Surface area of a cube:

\(SA = 6a^2\)

\(SA = 6(6)^2\)

What's 6 * 6? @~*Ashtyn*~

Answer 4

36

Answer 5

Yes, and what's 36 * 6?

Answer 6

@~*Ashtyn*~

Answer 7

216 (sorry I was helping someone in english xD) @iGreen.

Answer 8

No problem,

So the SA of the cube is 216.

Now let's find the SA of the rectangle:

\(SA=2(wl+hl+hw)\)

Plug in what we know:

\(SA=2((6)(14)+(8)(14)+(8)(6))\)

Simplify it

Answer 9

I'm confused -.-

Answer 10

Lol, you multiply 6 * 14, 8 * 14, and 8 * 6, then you add them up

Answer 11

Got it xD Thanks :)

Answer 12

So it is A right ?

Answer 13

@iGreen. or @iGreen

Answer 14

@iGreen. 's solution will give a result that is incorrect because it includes the area that is hidden between the cube and the prism.
If you use @iGreen. 's method, you must subtract 2 * 36 ft^2 from what he got to account for the areas of the cube ad the prism that are hidden.

Answer 15

Yeah, I was getting to that :P

Answer 16

Add up the three areas above to get your final answer.

Answer 17

SA = 296 ft^2 + 168 ft^2 + 168 ft^2

Answer 18

Now let's do it @iGreen. 's way, but being careful to subtract the hidden surfaces' areas.

Cube SA = 6 * 6 * 6 = 216 ft^2
Prism SA = 2(6 * 14 + 8 * 14 + 8 * 6) = 488 ft^2
Hidden SA = 2 * 6 * 6 = 72 ft^2

SA = 216 ft^2 + 488 ft^2 - 72 ft^2

Answer 19

Do the operations and compare the results.
Both methods work, but you must be careful to subtract the hidden areas.

Answer 20

Ummmm I already turned it in... So I am already done, Thanks SO much for your help though :)