anonymous
  • anonymous
A candy bar box is in the shape of a triangular prism. The volume of the box is 2,400 cubic centimeters.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 the sides of the candy box? Explain how you got your answer. (5 points)
Mathematics
katieb
  • katieb
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Zenshiru
  • Zenshiru
Hello, do you have a diagram you can show me for this question?
anonymous
  • anonymous
First of all, the formula for volume is: volume = base * height
anonymous
  • anonymous
So, using that equation, we can't solve for the height, since there are still 2 variables that we don't have values for.

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anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
this should help: http://www.mathwarehouse.com/solid-geometry/triangular-prism/images/triangular-prism-image-labelled.jpg
anonymous
  • anonymous
in this case the height is 20 because it's shown on the prism
anonymous
  • anonymous
wouldn't the height be seventeen if in the link you showed me "a" is the height? @ab854
anonymous
  • anonymous
No, for the link i gave you, "a" and "c" are both used to find the area of the trianlge, otherwise known as the Base of the prism
anonymous
  • anonymous
a would be the height of the triangle
anonymous
  • anonymous
ohh okay. So 16 would be the base of the box and 20 would be the height? @ab854
Zenshiru
  • Zenshiru
Actually, the height here is not shown. What we know from the question is: Volume= 2,400 cubic centimeters. Base= 16 cm. Length = 20 cm. We are looking for the height. To solve for the height let's rearrange the formula in terms of H. So it will look like this: V = 1/2(B*L*H)
anonymous
  • anonymous
so it would be 1/2(16*20*H) But we don't know the height. @Zenshiru
Zenshiru
  • Zenshiru
I'm working on a little picture, give me one moment. My crop tool is acting up.
anonymous
  • anonymous
okay
Zenshiru
  • Zenshiru
Alright, so using what I just said, you're able to rearrange your equation, and it should look something like this. You should be able to plug your given values into this.
anonymous
  • anonymous
so the height is fifteen?
Zenshiru
  • Zenshiru
Yep! The height of that figure is 15 cm.
anonymous
  • anonymous
okay thanks. I think I know what to do. Wouldn't you just find the circumference of the whole box?
anonymous
  • anonymous
I think it means all sides.
anonymous
  • anonymous
I found the lateral surface area. It's 795 cm
anonymous
  • anonymous
okay thank you for your help @Zenshiru ! is there anyone you know that can help me with part two?
anonymous
  • anonymous
Thank you so much!
anonymous
  • anonymous
|dw:1442700685039:dw|
anonymous
  • anonymous
surface are=120*2+2*20*17+20*16=240+680+320=1240 card board needed=1240 square cms.
anonymous
  • anonymous
Consider the following |dw:1442691552955:dw| Similarly for your prism we have |dw:1442691716775:dw|
anonymous
  • anonymous
|dw:1442691914287:dw|
anonymous
  • anonymous
In context of your question, \[b=16cm\]\[h=??\]\[l=20cm\]\[V=l \times \frac{1}{2} \times b \times h\] Calculate h using the 8,h,17 right triangle

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