Study Guide

Surface Area and Volume Introduction

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Surface Area and Volume Introduction

You and your friends have finally bought tickets to Zombie Apocalypse VII: Revenge of Lord Bloodlust, a movie rated NC-17 for its violence alone, and gory enough to be banned in 41 states (and counting). Your parents definitely don't approve…or at least they wouldn't if they had any idea you were going.

Luckily, they're out of town this weekend at a Zen retreat, and who are you to ruin that experience for them? Let them be one with nature. You've got some zombie-crushing to do.

As you and your friends find your seats in the crowded theater holding buttery popcorn and extra-large Icees, all your friends start pulling out their 3D glasses. You're not sure why, since you heard that the 3D version would be released only once the lawsuit against the director is settled. You ask your friends, and they tell you this is a special one-night-only screening in 3D before the case is taken to the Supreme Court. Unfortunately, you left your 3D glasses at home.

For the next two hours and forty-three minutes, you're subjected to images of blurry zombies attacking faceless heroes, an unclear mess of blood and guts, and fighting scenes that would have been epic had they not been in double vision. As the credits roll, you can't help but think of how you tricked your parents and that karma always has a way of catching up with you.

Three dimensions might catch you off-guard and, just like in Zombie Apocalypse VII, leave you confused, headachy, and bloody miserable. We've been working in two dimensions for so long that we might have forgotten that real life exists in three.

Fear not. Unlike your experience with Zombie Apocalypse VII, prolonged exposure to the third dimension (à la volumes and surface areas) won't have you wanting to tear your own eyes out. And we certainly won't have zombies wanting to tear your eyes out. Well, not as long as we keep some weapons and antidote at the ready.

Surface Area and Volume Resources


3D Shapes
An interactive site that helps you visualize pretty much any 3D shape you'll ever need. If nets have got you in a tangled mess, you can take a gander at them and cut yourself loose. Rotate the solids and you'll be counting edges, vertices, and faces instead of sheep to fall asleep at night.

Basic Mathematics: Volume
This nifty website will clearly go through every shape and explain how to calculate its volume. It also has some fun math games at the bottom that you can procrastinate with.

Surface Area and Volume Quiz
By now, you've got some mad surface area and volume skillz. Use this quick 6-question quiz and test yourself to see how awesome your geometry chops really are. We're sure you'll ace it, no problem.


How to Turn a Sphere Inside Out
Have you ever wanted to turn a sphere inside out? If you think it can't be done, just take a look at this.

Volume and Surface Area
A clear and easy-to-understand visualization of the surface areas and volumes of some essential shapes. It's also set to some groovy music, so turn up the volume (get it?) and take a dance break while you're at it.

Plotting Points in 3D
If plotting points in three dimensions seems like something for a rocket scientist, this video's got your back. It will explain everything you need to know to get started working in the third dimension, from point-plotting to distance-finding to midpoint-calculating. Before you know it, you'll have a third degree in the third dimension.

Games and Tools

Illuminations: Geometric Solids
This interactive tool lets you play with Platonic solids. You can rotate them, enlarge them, and even create your own nets to print out and fold up. Like a marriage counselor between you and surface areas, it'll help you understand each other better. Together, you'll build a solid (relationship).

Volume Shape Shoot Game
How voluminous is your knowledge of 3D shapes? Earn points by clicking on the flying solids. Sit back, relax, and click when the spirit moves you, or be a daredevil and select timed mode. Whatever tickles your fancy. Be careful, though, since you lose points by clicking on the wrong solid.

Surface Area Calculator
Now that you know what it takes to find the surface area, you can leave it up to a calculator. Just select the shape you need, input the measurements, and presto! And if you want a refresher on the actual formulas used, just scroll down.

Volume Calculator
When heights and cubic units have got you down, just pop in the solid's values into a volume calculator and let it do the work for you. The formulas are all spelled out below too, just in case you want to take a crack at volume the old-fashioned way.

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