Question

one link in a chain was made from a cylinder that has a radius of 2.5 cm and a height of 22 cm. how much plastic coating would be needed to coat the surface of the chain link? use 3.14 for π.
251.2 cm²
314 cm²
345.4 cm²
471 cm²

Explanation:

Step1: Recall surface - area formula for cylinder

The surface - area formula of a cylinder is $S = 2\pi r^2+2\pi rh$, where $r$ is the radius and $h$ is the height.

Step2: Substitute given values

Given $r = 2.5$ cm and $h=22$ cm, and $\pi = 3.14$. First, calculate $2\pi r^2$:
$2\times3.14\times(2.5)^2=2\times3.14\times6.25 = 39.25$ $cm^2$.
Then, calculate $2\pi rh$:
$2\times3.14\times2.5\times22= 345.4$ $cm^2$.

Step3: Find total surface area

$S=2\pi r^2 + 2\pi rh=39.25+345.4 = 384.65$ $cm^2$. But if we assume the chain - link is a hollow - like structure and we only consider the outer - surface area and neglect the two circular ends (a possible interpretation as the problem may not want to double - count some areas), we can use the lateral - surface area formula $S = 2\pi rh$.
$S=2\times3.14\times2.5\times22=345.4$ $cm^2$.

Answer:

$345.4$ $cm^2$