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 the surface - area formula for a 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 one circular base is $A_{base}=\pi r^{2}$. Given $r = 2.5$ cm, then $A_{base}=3.14\times(2.5)^{2}=3.14\times6.25 = 19.625$ $cm^{2}$. The area of two circular bases is $2\times19.625=39.25$ $cm^{2}$.

Step3: Calculate the lateral - surface area

The lateral - surface area formula is $A_{lateral}=2\pi rh$. Given $r = 2.5$ cm and $h = 22$ cm, then $A_{lateral}=2\times3.14\times2.5\times22= 345.4$ $cm^{2}$.

Step4: Calculate the total surface area

The total surface area $S=A_{base - total}+A_{lateral}=39.25 + 345.4=384.65$ $cm^{2}$. But there seems to be an error in the problem - setup as the options provided do not match with the correct calculation. If we assume we only consider the lateral - surface area (maybe the bases are not to be coated), then the amount of plastic coating needed is $A = 2\pi rh=2\times3.14\times2.5\times22 = 345.4$ $cm^{2}$.

Answer:

$345.4$ $cm^{2}$