One link in a chain was made from a cylinder that has a radius of 3 cm and a height of 25 cm. How much plastic coating would be needed to coat the surface of the chain link? Use 3.14 for [tex]$\pi$[/tex].
Answer (2)
Calculate the area of the two circular bases: 2 × 3.14 × 3 2 = 56.52 cm 2 .
Calculate the lateral surface area: 2 × 3.14 × 3 × 25 = 471 cm 2 .
Add the base area and lateral area to find the total surface area: 56.52 + 471 = 527.52 cm 2 .
The amount of plastic coating needed is: 527.52 cm 2 .
Explanation
Problem Analysis We are given a cylinder with a radius of 3 cm and a height of 25 cm. We need to find the surface area of this cylinder, which represents the amount of plastic coating needed. We will use the formula for the surface area of a cylinder, which is the sum of the areas of the two circular bases and the lateral surface area. We are also given that we should use 3.14 as the value for π .
Calculate the area of the two bases First, let's calculate the area of the two circular bases. The area of one base is π r 2 , so the area of two bases is 2 π r 2 . Substituting r = 3 cm and π = 3.14 , we get: 2 × 3.14 × 3 2 = 2 × 3.14 × 9 = 56.52 cm 2
Calculate the lateral surface area Next, let's calculate the lateral surface area of the cylinder. The formula for the lateral surface area is 2 π r h . Substituting r = 3 cm, h = 25 cm, and π = 3.14 , we get: 2 × 3.14 × 3 × 25 = 471 cm 2
Calculate the total surface area Now, let's add the area of the two bases and the lateral surface area to find the total surface area: 56.52 + 471 = 527.52 cm 2
Final Answer Therefore, the amount of plastic coating needed to coat the surface of the chain link is 527.52 cm 2 .
Examples
Imagine you're designing a cylindrical storage container for your desk. Knowing how to calculate the surface area helps you determine how much material you need to cover the container, ensuring you have enough to complete your project without waste. This is a practical application of surface area calculations in everyday life.
The total surface area of the chain link, calculated from the cylinder's dimensions, is 527.52 cm 2 . This includes the areas of the two bases and the lateral surface. Therefore, this is the amount of plastic coating required.
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