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)

- anonymous

- katieb

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- Zenshiru

Hello, do you have a diagram you can show me for this question?

- anonymous

First of all, the formula for volume is: volume = base * height

- 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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## More answers

- anonymous

##### 1 Attachment

- anonymous

this should help: http://www.mathwarehouse.com/solid-geometry/triangular-prism/images/triangular-prism-image-labelled.jpg

- anonymous

in this case the height is 20 because it's shown on the prism

- anonymous

wouldn't the height be seventeen if in the link you showed me "a" is the height? @ab854

- 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

a would be the height of the triangle

- anonymous

ohh okay. So 16 would be the base of the box and 20 would be the height? @ab854

- 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

so it would be 1/2(16*20*H) But we don't know the height. @Zenshiru

- Zenshiru

I'm working on a little picture, give me one moment. My crop tool is acting up.

- anonymous

okay

- 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.

##### 1 Attachment

- anonymous

so the height is fifteen?

- Zenshiru

Yep! The height of that figure is 15 cm.

- anonymous

okay thanks. I think I know what to do. Wouldn't you just find the circumference of the whole box?

- anonymous

I think it means all sides.

- anonymous

I found the lateral surface area. It's 795 cm

- anonymous

okay thank you for your help @Zenshiru ! is there anyone you know that can help me with part two?

- anonymous

Thank you so much!

- anonymous

|dw:1442700685039:dw|

- anonymous

surface are=120*2+2*20*17+20*16=240+680+320=1240
card board needed=1240 square cms.

- anonymous

Consider the following
|dw:1442691552955:dw|
Similarly for your prism we have
|dw:1442691716775:dw|

- anonymous

|dw:1442691914287:dw|

- 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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