Question

one link in a chain was made from a cylinder that has a radius of 2 cm and a height of 20 cm. how much plastic coating would be needed to coat the surface of the chain link? use 3.14 for π.
471 cm²
345.4 cm²
314 cm²
251.2 cm²

Explanation:

Step1: Recall surface - area formula for cylinder

The surface - area formula of a cylinder is $S = 2\pi r^2+2\pi rh$.

Step2: Calculate the area of the two circular bases

The area of a single circular base is $A_{base}=\pi r^2$. Given $r = 2$ cm, then $A_{base}=3.14\times2^2=3.14\times4 = 12.56$ $cm^2$. The area of two circular bases is $2A_{base}=2\times12.56 = 25.12$ $cm^2$.

Step3: Calculate the lateral - surface area

The lateral - surface area of a cylinder is $A_{lateral}=2\pi rh$. Given $r = 2$ cm and $h = 20$ cm, then $A_{lateral}=2\times3.14\times2\times20=251.2$ $cm^2$.

Step4: Calculate the total surface area

The total surface area $S=2\pi r^2 + 2\pi rh=25.12+251.2=276.32$ $cm^2$. But if we assume the chain - link is a non - closed cylinder (open at the top and bottom for linking purposes), we only consider the lateral surface area. So the plastic coating needed is $251.2$ $cm^2$.

Answer:

$251.2$ $cm^2$