*Yuanxin (Amy) Yang Alcocer*Show bio

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*
Show bio

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Although it may seem to be just a mathematical activity, the surface-area-to-volume ratio actually has real-world significance. In this lesson, you'll learn how you can calculate this ratio along with how useful this ratio is in various aspects of science.

All shapes, including our bodies, have a surface area. A **surface area** is the area of the object that's exposed on the outside. So, for your body, it's how much skin you have. For a cube, it's the total area of all six sides of the cube. In math, geometric shapes have specific formulas you can use to calculate their surface areas.

A cube has a surface area of 6s2 and a sphere has a surface area of 4 * pi * r2.

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These same three-dimensional geometric shapes also have formulas for volume. The **volume** is the space inside the shape. Only three-dimensional shapes have volume. Two-dimensional shapes, such as a line or a square, don't have volume. If it helps, you can think of volume as how much liquid would fit inside a shape.

The formula for the volume of a cube is s3.

For the sphere, the volume is 4/3 * pi * r3.

These formulas make it very easy to find the surface area and volume of these shapes. For other shapes, more complicated math such as integral calculus may be needed. For this lesson, though, you won't need to know calculus, just the formulas that are available for common shapes.

When you divide surface area by volume, you get a special ratio called the **surface-area-to-volume ratio**. This ratio can be noted as SA:V.

To use this ratio, you can plug in the value for your variable and then calculate your ratio. So, if your cube has a side length of 1 centimeter with a volume of 1 cubic centimeter, then your surface-area-to-volume ratio is 6 / 1 = 6. The only thing you needed to do is to plug in your value for the length of your side.

Let's try calculating the surface-area-to-volume ratio for the sphere.

To calculate this ratio for the sphere, you do the same as you did for the cube. You take the formula for surface area and you divide it by the formula for volume. This is what you get:

You use this ratio the same as you would for the cube. If you have a radius of 1 centimeter for a volume of 4.187 cubic centimeters, then your surface-area-to-volume ratio is 3 / 1 = 3. All you have to do is plug in your value for the radius.

**Surface area** is how much area of the object is exposed to the outside. The **volume** is how much space is inside the shape. The **surface-area-to-volume ratio** tells you how much surface area there is per unit of volume. This ratio can be noted as SA:V. To find this ratio, you divide the formula for surface area by the formula for volume and then you simplify. If you are given the numbers, then you simply divide the surface area number by the volume number.

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