tahtah99
Observe the composite figure below.
The bottom shape is a cube with base edges of 16 meters. The top shape is a right pyramid with a height of 15 meters. What is the surface area of this composite figure?
Answer
544 m2
1,280 m2
1,824 m2
2,080 m2
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tahtah99
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darthsid
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What's your working so far? How are you approaching this?
tahtah99
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i have made it absolutely no where on this problem.
darthsid
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Do you know what the area of a square is?
tahtah99
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yesss
darthsid
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Great! So try to divide the figure into two parts:
1. the pyramid
2. The cube
darthsid
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Now, a cube's surface is basically 6 squares, so what would the area of the surface of the cube be?
tahtah99
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256???
darthsid
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That's the area of one square. A cube's surface is made of 6 squares. So the surface area of the cube is 6 times the area of a square, right?
tahtah99
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so that would be 1,536
darthsid
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Yeah, so that's the surface area of the bottom part.
Now let us look at the top part, it is a right pyramid, which is basically 4 triangles and a square on the surface
darthsid
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DO you have the formula for the surface area of a right pyramid?
tahtah99
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B+ 1/2ps?
kk1022
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yes
darthsid
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Exactly, for the pyramid your main problem is finding s
what's the formula for s?
You're very close!
tahtah99
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i have no idea ! haha
darthsid
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B is the area of the base, which is a square, which you calculated above was 256! P is the perimeter of the base, which is the sum of all sides of the base,
So P = 16 + 16 + 16 + 16 = 64
darthsid
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So we are left with s, which is the slant height. Slant height
\[s=\sqrt{{h^2}+{r^2}}\]
where h is the height, and r is the radius of the base
The radius of the base is half the side of the square, so r = 8.
Can you calculate s?
tahtah99
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289?
tahtah99
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17
kk1022
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nno 288
kk1022
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16
darthsid
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No no, square root that! You are on the right track tahtah99 :)
darthsid
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yess, 17!
darthsid
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So, you said the formula was
B + 1/2Ps
B = 256 (area of square)
P = 64 (perimeter of square)
s = 17
So total surface area of the pyramid is?
tahtah99
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800 ?
darthsid
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Great! That's correct.
kk1022
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see i told you!!
kk1022
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you got it!!
tahtah99
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-_____- hahah
darthsid
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So now, you have a pyramid and a cube
Area of pyramid = 800
Area of cube = 1536
Now if you join the two, you will not see one side of the cube, and the base of the pyramid. Do you understand that?
darthsid
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It's not done yet :D
kk1022
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dont celebrate, its not done yet!!
tahtah99
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oh Lord..
yeah i understand
darthsid
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So you have to subtract the area of two things:
1. The base of the pyramid
2. One square from the cube.
tahtah99
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so subtract 512?
darthsid
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So your final area will be:
1536 + 800 - (area of 1 square) - (area of 1 square)
= 1536 + 800 - 256 - 256
darthsid
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Exactly! You got this!
kk1022
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exactly!! WHAT I SAY?? YOU GOT IT!
tahtah99
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is the answer c?
kk1022
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THATS WHAT IVE BEEN TRYING TO SAY!! YES IT IS!!!!!!
darthsid
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Yes it is!
darthsid
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Congrats :)
tahtah99
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thank you so much ! : )
kk1022
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SEE! NOOOOOWWW YOU CELEBRATE!!
kk1022
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YOUR VERY WELCOME~!
tahtah99
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hahahahahahha
darthsid
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Glad to help!
kk1022
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glad to help too!
tahtah99
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could you check my answer for the last question ?
tahtah99
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nvm got it
kk1022
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ok.