Modern metal cans, like the one shown, are usually made from steel, and
then covered with a thin layer of tin. Write an inequality representing the amount of sheet metal that can be
used to make a can that is 10 cm tall
To write an inequality representing the amount of sheet metal that can be used to make a can that is 10 cm tall, we need to consider the surface area of the can.
The surface area of a cylindrical can consists of the area of the top, the area of the bottom, and the area of the side. Let's denote the radius of the can as "r" and the height as "h". Given that the can is cylindrical, we can calculate the surface area as follows:
Area of top and bottom (circular): 2πr²
Area of side (rectangular): 2πrh
Since we want to represent the amount of sheet metal used in the can, the inequality can be written as:
Sheet metal used ≤ total surface area
The total surface area is obtained by adding the areas of the top, bottom, and side:
Total surface area = 2πr² + 2πrh
Therefore, the inequality representing the amount of sheet metal that can be used to make a can that is 10 cm tall is:
Sheet metal used ≤ 2πr² + 2πrh
To further simplify the inequality, you would need more specific information about the can's size, material thickness, and any constraints on the design.