Question

compare the volume and surface area of a cylinder. sort each description into the appropriate category. represents the amount of space an object takes up found by multiplying the area of a base by the height use this to find the amount to fill something represents the area of the outside surface of the object found by adding the areas of the 2 bases and the area of the lateral surface use this to find how much is needed to cover something volume surface area

Explanation:

Volume

• represents the amount of space an object takes up: This is the fundamental definition of volume.
• found by multiplying the area of a base by the height: The formula for the volume of a cylinder \(V = B\times h\) (where \(B\) is the area of the base and \(h\) is the height).
• use this to find the amount to fill something: Volume measures the capacity, so it tells how much a container can hold.

Surface Area

• represents the area of the outside surface of the object: Surface area is about the outer covering.
• found by adding the areas of the 2 bases and the area of the lateral surface: The formula \(SA=2\pi r^{2}+ 2\pi rh\) (where \(2\pi r^{2}\) is the area of the two bases and \(2\pi rh\) is the lateral surface area).
• use this to find how much is needed to cover something: Surface area is used to determine the amount of material for covering.

Answer:

• Volume: represents the amount of space an object takes up, found by multiplying the area of a base by the height, use this to find the amount to fill something.
• Surface Area: represents the area of the outside surface of the object, found by adding the areas of the 2 bases and the area of the lateral surface, use this to find how much is needed to cover something.