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# Surface Area to Volume Ratio

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Author: Susan Rodriguez

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Tutorial

## Hot Air Balloons

Source: Patrick Smith

## A Little Math First

Hot air balloons are large vessels.  The reason engineers make them so large is NOT so that they are easier to see way up in the sky.  The reason they are so large is based on Math.  The surface area to volume ratio must be close to 1:1. Whoa!  What does that mean?!  Let's explore this together

## Finding the Surface Area of a Cube

Source: Mahalo.com

## Finding the Volume of a Cube

Source: Mahalo.com

## But, why?

Why does the Surface Area to Volume ratio need to be closer to 1:1?

Surface area represents the weight of the envelope. It is heavier than air and pushes down to earth.

Volume represents the hot air inside the balloon. Since hot air is less dense than the cold air around it, it lifts up.

So,a balloon will gain lift when the volume of hot air inside is the same or greater than the weight of the envelope surrounding it.

## Let's Try It

Download the worksheet and use the blocks provided in the Math Center.

As you create models of hot air balloons, think about the ratio of surface area to volume.

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## Surface Area to Volume Ratio

This ratio is important because it will tell you how much lift your balloon will have.  The smaller the ratio, the better your balloon will fly!  If your balloon won't fly you may need more volume compared to your surface area.

Click on the activity below and practice finding volume, surface area, and the surface area to volume ratio.

Activity