## nuccioreggie one year ago A candy bar box is in the shape of a triangular prism. The volume of the box is 3,240 cubic centimeters. A triangular prism is shown with base of triangle labeled 24 cm, sides of the triangle labeled 15 cm, and length of the box equal to 30 cm. Part A: What is the height of the box? Show your work. (5 points) Part B: What is the approximate amount of cardboard used to make this candy box? Explain how you got your answer. (5 points)

1. nuccioreggie

2. nuccioreggie

@Michele_Laino

3. Here_to_Help15

lol your doing this on android ?

4. nuccioreggie

Lol yea lololl

5. nuccioreggie

@Michele_Laino. Can you explain the answer

6. alekos

VOLUME = 1/2 base x height x length

7. Michele_Laino

the area of the base of your prism, is the area of a triangle whose base and height are 24cm and 15 cm respectively. SO the area of the base of your prism is: A=(24*15)/2=...cm^2

8. Michele_Laino

So*

9. nuccioreggie

Thats the answer for a and b ?

10. Michele_Laino

it is the first step for part A

11. nuccioreggie

Whats B?

12. nuccioreggie

Ok whats the next step for part A

13. Michele_Laino

what is the base area? please continue my computation

14. nuccioreggie

Ok so wait is is 180^2cm ?? Right

15. Michele_Laino

ok!

16. Michele_Laino

now we can write: volume = base area x height of prism so, we get: $3240 = 180 \times H$ what is H?

17. nuccioreggie

24cm

18. Michele_Laino

are you sure? 24*180=4320

19. nuccioreggie

15cm?

20. Michele_Laino

what is: 3240/180=...?

21. nuccioreggie

180 @Michele_Laino

22. nuccioreggie

@I ment its 18

23. Michele_Laino

ok! So the height of your prism is H=18 cm

24. nuccioreggie

Ok so i have to do 180x18?

25. Michele_Laino

|dw:1433958517323:dw|

26. nuccioreggie

I got 3240 when i did 180×18=3240

27. Michele_Laino

ok!

28. nuccioreggie

the area of the base of the prism, is the area of a triangle whose base and height is 24cm and 15 cm respectively. So the area of the base of the prism is: A=(24*15)/2= 180^2cm Ok so then now i can write: volume = base area x height of prism so, then i get: 3240=180×18=3240 Thats what i got so far is that correct

29. nuccioreggie

@Michele_Laino. Can we do B now my friend

30. Michele_Laino

for part B, we have to compute the area of total surface of your prism

31. nuccioreggie

Ok can you explain that answer for me so it will be faste and easier

32. Michele_Laino

we have two triangles, and the area of each triangle is 180 cm^2, so the base area of your prism is: 180*2=...

33. Michele_Laino

34. nuccioreggie

360

35. Michele_Laino

ok! Now the area of lateral surface is: base perimeter x height

36. Michele_Laino

|dw:1433959057271:dw|

37. nuccioreggie

So i have to do 15×24 now?

38. Michele_Laino

in order to compute the base perimeter, we have to compute the sides of that triangle, first

39. Michele_Laino

|dw:1433959149838:dw|

40. nuccioreggie

Can u write it out for me i dont understand

41. Michele_Laino

using the theorem of Pitagora, we can write: $\Large AC = \sqrt {C{H^2} + A{H^2}} = \sqrt {{{15}^2} + {{12}^2}} = ...$

42. nuccioreggie

Can you write the whole answer out for me for part B because. So i will understand much better

43. Michele_Laino

no, I can not give you the direct answer, since I have to respect the Code Of Conduct

44. nuccioreggie

Your not your EXPLAING THE ANSER TO ME SO I WILL UNDERSTAND MUCH BETTER

45. Michele_Laino

please, what is AC? continue my computation

46. nuccioreggie

Idk

47. Michele_Laino

what is: $\Large \sqrt {{{15}^2} + {{12}^2}} = ...$?

48. nuccioreggie

4

49. Michele_Laino

50. nuccioreggie

I cant

51. nuccioreggie

52. Michele_Laino

use an online calculator then

53. nuccioreggie

27

54. Michele_Laino

no, here is an online calculator: http://www.wolframalpha.com/

55. nuccioreggie

Im trying to tell u it dosnt work for me somthing is wrong with my computer

56. nuccioreggie

159?

57. Michele_Laino

here is the value of AC AC=19.21 cm so the base perimeter is: 19.21+24+19.21=...

58. nuccioreggie

62.42

59. nuccioreggie

@Michele_Laino

60. nuccioreggie

@Michele_Laino. Its 62.42 is that right

61. Michele_Laino

ok!: so the lateral surface is: 64.42* 18=...?