anonymous 4 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

1. anonymous

2. darthsid

What's your working so far? How are you approaching this?

3. anonymous

i have made it absolutely no where on this problem.

4. darthsid

Do you know what the area of a square is?

5. anonymous

yesss

6. darthsid

Great! So try to divide the figure into two parts: 1. the pyramid 2. The cube

7. darthsid

Now, a cube's surface is basically 6 squares, so what would the area of the surface of the cube be?

8. anonymous

256???

9. darthsid

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. anonymous

so that would be 1,536

11. darthsid

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

DO you have the formula for the surface area of a right pyramid?

13. anonymous

B+ 1/2ps?

14. anonymous

yes

15. darthsid

Exactly, for the pyramid your main problem is finding s what's the formula for s? You're very close!

16. anonymous

i have no idea ! haha

17. darthsid

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

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. anonymous

289?

20. anonymous

17

21. anonymous

nno 288

22. anonymous

16

23. darthsid

No no, square root that! You are on the right track tahtah99 :)

24. darthsid

yess, 17!

25. darthsid

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. anonymous

800 ?

27. darthsid

Great! That's correct.

28. anonymous

see i told you!!

29. anonymous

you got it!!

30. anonymous

-_____- hahah

31. darthsid

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

It's not done yet :D

33. anonymous

dont celebrate, its not done yet!!

34. anonymous

oh Lord.. yeah i understand

35. darthsid

So you have to subtract the area of two things: 1. The base of the pyramid 2. One square from the cube.

36. anonymous

so subtract 512?

37. darthsid

So your final area will be: 1536 + 800 - (area of 1 square) - (area of 1 square) = 1536 + 800 - 256 - 256

38. darthsid

Exactly! You got this!

39. anonymous

exactly!! WHAT I SAY?? YOU GOT IT!

40. anonymous

41. anonymous

THATS WHAT IVE BEEN TRYING TO SAY!! YES IT IS!!!!!!

42. darthsid

Yes it is!

43. darthsid

Congrats :)

44. anonymous

thank you so much ! : )

45. anonymous

SEE! NOOOOOWWW YOU CELEBRATE!!

46. anonymous

47. anonymous

hahahahahahha

48. darthsid

49. anonymous

50. anonymous

could you check my answer for the last question ?

51. anonymous

nvm got it

52. anonymous

ok.