Imagine that you have a pitcher of water, and you want to fill it all the way up. How much water will it hold? If your pitcher is shaped like a cylinder, it will be pretty easy to figure this out before you ever put a single drop of water into the pitcher. The total amount of space inside an object like your pitcher is called its volume.
What if you now decided you wanted to paint the outside of the pitcher a different color? How much paint would you need to use to cover the whole outer surface of the pitcher. The area of the surface of an object is called its surface area.
For simple geometric shapes like spheres, cylinders, and prisms, it's pretty easy to calculate both the volume and surface area, as you can see with these formulas and their images.
Definitions of surface area and volume for a sphere, cylinder, and rectangular prism
Surface area and volume definitions
As the object gets bigger, it makes sense that both surface area and volume would get bigger, too. However, can you guess which one will get bigger faster? For example, if you double the radius of a sphere, will the volume also double? What about the surface area? Which one will increase the most or will they increase the same amount? Let's look at a few examples and see if we can come up with some general rules for how changes in dimensions will affect the surface area and volume of an object.
Answers & Comments
Answer:
What Are Surface Area & Volume?
Imagine that you have a pitcher of water, and you want to fill it all the way up. How much water will it hold? If your pitcher is shaped like a cylinder, it will be pretty easy to figure this out before you ever put a single drop of water into the pitcher. The total amount of space inside an object like your pitcher is called its volume.
What if you now decided you wanted to paint the outside of the pitcher a different color? How much paint would you need to use to cover the whole outer surface of the pitcher. The area of the surface of an object is called its surface area.
For simple geometric shapes like spheres, cylinders, and prisms, it's pretty easy to calculate both the volume and surface area, as you can see with these formulas and their images.
Definitions of surface area and volume for a sphere, cylinder, and rectangular prism
Surface area and volume definitions
As the object gets bigger, it makes sense that both surface area and volume would get bigger, too. However, can you guess which one will get bigger faster? For example, if you double the radius of a sphere, will the volume also double? What about the surface area? Which one will increase the most or will they increase the same amount? Let's look at a few examples and see if we can come up with some general rules for how changes in dimensions will affect the surface area and volume of an object.
Step-by-step explanation:
Its true