Certainly! Let's solve the problem step-by-step:
The problem asks for the amount of plastic coating needed for one link in a chain, which is made from a cylinder with a radius of 2.5 cm and a height of 22 cm. Essentially, we need to find the surface area of this cylinder.
The surface area [tex]\( A \)[/tex] of a cylinder can be found using the formula:
[tex]\[ A = 2\pi r^2 + 2\pi rh \][/tex]
where:
- [tex]\( r \)[/tex] is the radius of the cylinder,
- [tex]\( h \)[/tex] is the height of the cylinder,
- [tex]\( \pi \)[/tex] (pi) is approximately 3.14159.
Given:
- Radius [tex]\( r = 2.5 \)[/tex] cm
- Height [tex]\( h = 22 \)[/tex] cm
Substitute these values into the formula:
1. Calculate the area of the two circular bases:
[tex]\[ 2\pi r^2 = 2 \times \pi \times (2.5)^2 \][/tex]
2. Calculate the area of the cylindrical surface:
[tex]\[ 2\pi rh = 2 \times \pi \times 2.5 \times 22 \][/tex]
Sum these areas to get the total surface area:
[tex]\[ A = 2\pi (2.5)^2 + 2\pi (2.5 \times 22) \][/tex]
Using the values given, the total surface area comes out to approximately 384.84510006474966 square centimeters.
Since the problem does not explicitly ask for rounding and the closest provided multiple choice answer is among the given options, the correct answer to the question is:
[tex]\[ 384.845 \text{ cm}^2 \][/tex]
However, this option is not listed correctly among the multiple choices. This discrepancy suggests a potential issue in the problem's options. The correct step-by-step solution leads us to the result of around 384.845 cm², but you should communicate this finding to your instructor.
Thus, based on the calculation and the closest available options:
None of the given options match the accurate calculated result precisely. Make sure to contact the instructor to address this mismatch.
