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tahtah99

  • 2 years ago

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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  1. tahtah99
    • 2 years ago
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  2. darthsid
    • 2 years ago
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    What's your working so far? How are you approaching this?

  3. tahtah99
    • 2 years ago
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    i have made it absolutely no where on this problem.

  4. darthsid
    • 2 years ago
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    Do you know what the area of a square is?

  5. tahtah99
    • 2 years ago
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    yesss

  6. darthsid
    • 2 years ago
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    Great! So try to divide the figure into two parts: 1. the pyramid 2. The cube

  7. darthsid
    • 2 years ago
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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?

  8. tahtah99
    • 2 years ago
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    256???

  9. darthsid
    • 2 years ago
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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?

  10. tahtah99
    • 2 years ago
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    so that would be 1,536

  11. darthsid
    • 2 years ago
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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

  12. darthsid
    • 2 years ago
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    DO you have the formula for the surface area of a right pyramid?

  13. tahtah99
    • 2 years ago
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    B+ 1/2ps?

  14. kk1022
    • 2 years ago
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    yes

  15. darthsid
    • 2 years ago
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    Exactly, for the pyramid your main problem is finding s what's the formula for s? You're very close!

  16. tahtah99
    • 2 years ago
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    i have no idea ! haha

  17. darthsid
    • 2 years ago
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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

  18. darthsid
    • 2 years ago
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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?

  19. tahtah99
    • 2 years ago
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    289?

  20. tahtah99
    • 2 years ago
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    17

  21. kk1022
    • 2 years ago
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    nno 288

  22. kk1022
    • 2 years ago
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    16

  23. darthsid
    • 2 years ago
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    No no, square root that! You are on the right track tahtah99 :)

  24. darthsid
    • 2 years ago
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    yess, 17!

  25. darthsid
    • 2 years ago
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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?

  26. tahtah99
    • 2 years ago
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    800 ?

  27. darthsid
    • 2 years ago
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    Great! That's correct.

  28. kk1022
    • 2 years ago
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    see i told you!!

  29. kk1022
    • 2 years ago
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    you got it!!

  30. tahtah99
    • 2 years ago
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    -_____- hahah

  31. darthsid
    • 2 years ago
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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?

  32. darthsid
    • 2 years ago
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    It's not done yet :D

  33. kk1022
    • 2 years ago
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    dont celebrate, its not done yet!!

  34. tahtah99
    • 2 years ago
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    oh Lord.. yeah i understand

  35. darthsid
    • 2 years ago
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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.

  36. tahtah99
    • 2 years ago
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    so subtract 512?

  37. darthsid
    • 2 years ago
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    So your final area will be: 1536 + 800 - (area of 1 square) - (area of 1 square) = 1536 + 800 - 256 - 256

  38. darthsid
    • 2 years ago
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    Exactly! You got this!

  39. kk1022
    • 2 years ago
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    exactly!! WHAT I SAY?? YOU GOT IT!

  40. tahtah99
    • 2 years ago
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    is the answer c?

  41. kk1022
    • 2 years ago
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    THATS WHAT IVE BEEN TRYING TO SAY!! YES IT IS!!!!!!

  42. darthsid
    • 2 years ago
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    Yes it is!

  43. darthsid
    • 2 years ago
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    Congrats :)

  44. tahtah99
    • 2 years ago
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    thank you so much ! : )

  45. kk1022
    • 2 years ago
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    SEE! NOOOOOWWW YOU CELEBRATE!!

  46. kk1022
    • 2 years ago
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    YOUR VERY WELCOME~!

  47. tahtah99
    • 2 years ago
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    hahahahahahha

  48. darthsid
    • 2 years ago
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    Glad to help!

  49. kk1022
    • 2 years ago
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    glad to help too!

  50. tahtah99
    • 2 years ago
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    could you check my answer for the last question ?

  51. tahtah99
    • 2 years ago
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    nvm got it

  52. kk1022
    • 2 years ago
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    ok.

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