The part of a cube one: 1/8 or 1/6?

Test Preparation
1

<p>I put 1/8. Am I wrong?</p>

2

<p>you are right.</p>

3

<p>I tried using variables at first, then I realized that it was inefficient when I could just plug in random numbers for the side of the cube- I plugged in 2, therefore the volume of the cube is 8, and the volume of the triangular prism that resulted was 1. 1/8.</p>

4

<p>I just lookes at the top of the cube and saw that the triangle made at the top fit into the top face of the cube 8 times.</p>

5

<p>was this the midpoint one</p>

6

<p>yes actually just by looking is good but there is a way to do it as well..i will post it later. bt can u use rulers on the tests? can really help many ppl out</p>

7

<p>Here would be how to do it algebraically.</p>

<p>Let each side of the cube = 2x. Thus, the area of the entire cube is (2x)^3, which is 8x^3.</p>

<p>The area of the triangle on one face of the cube is (1/2)(x)(x) = (1/2)(x^2). Now multiply that by the height of the cube (2x) to get the area of the prism:</p>

<p>(1/2)(x^2)(2x) = x^3</p>

<p>So, (x^3)/(8x^3) = 1/8</p>

8

<p>you could use the speical triangle formula but that took me longer.</p>

9

<p>I just did it visually and thoght about it..
i got 1/8</p>

<p>only took me like 30 secs to think of it.</p>