Question

question 2 (multiple choice worth 4 points)
(06.04 mc)
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 π
o 251.2 cm²
o 314 cm²
o 345.4 cm²
o 471 cm²

Explanation:

Step1: Calculate the lateral surface area of the cylinder

The formula for the lateral surface area of a cylinder is \(2\pi rh\). Given \(r = 3\) cm and \(h=25\) cm, and \(\pi = 3.14\).

$$2\times3.14\times3\times25$$

$$=6.28\times3\times25$$

$$ = 18.84\times25$$

$$=471$$

Step2: Calculate the area of the two circular ends

The formula for the area of a circle is \(\pi r^{2}\). For two circles, it is \(2\pi r^{2}\).

$$2\times3.14\times3^{2}$$

$$=6.28\times9$$

$$= 56.52$$

Step3: Calculate the total surface area

The total surface area of the cylinder \(S=2\pi rh + 2\pi r^{2}\)

$$S=471+56.52$$

$$S = 527.52$$

(This step - by - step seems wrong as per the options. Wait, maybe it's a mis - understanding. Wait, if it's a chain - link (assuming it's a 3D shape approximated as a cylinder for coating). But looking at the options, maybe it's a wrong approach. Wait, no, wait the formula for the surface area of a cylinder \(A = 2\pi r(r + h)\)

$$A=2\times3.14\times3\times(3 + 25)$$

$$=6.28\times3\times28$$

$$=18.84\times28$$

$$=527.52$$

(Still not matching. Wait, no, maybe the problem is to find the lateral surface area only (if the coating is only on the side, but the options have 471. If we consider only the lateral surface area \(A_{l}=2\pi rh\)

$$A_{l}=2\times3.14\times3\times25$$

$$=471$$

Answer:

\(471\space cm^{2}\) (i.e., the first option \(471\space cm^{2}\))