# Cuboid Challenge

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Note by Llewellyn Sterling
3 years, 2 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

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Let the square base have sides =x and height = h. V=x * x * h. But if paper is L * L, x=L-2h. $$So~~ V=(L^2-4Lh+4h^2) * h.\\\dfrac{dV}{dh}=L^2-8Lh+12h^2=0 ~~~\implies 12h^2-8hL+L^2 \\For~~max~~h=\dfrac{8L-\sqrt{64^2-48L^2}}{24}=\dfrac L 6.~~\implies~ x= L-2*\dfrac L 6=\dfrac {2L}{3}...\large....x=\dfrac {2L}{3} ~~~~h=\dfrac L 6.$$

- 3 years, 2 months ago