Question

a company needs to produce a label that will wrap around the lateral side of a cylindrical can. if the can is 13 cm tall and has a diameter of 10.6 cm, what is the area of the label that the company needs to produce? enter a decimal rounded to the hundredths place. show your work here hint: to add the pi symbol (π), type \pi\

Explanation:

Step1: Find the circumference of the base

The formula for the circumference of a circle is \(C = \pi d\). Given \(d = 10.6\) cm, so \(C=\pi\times10.6\approx3.14\times10.6 = 33.284\) cm.

Step2: Calculate the lateral surface area

The formula for the lateral surface area of a cylinder is \(A = Ch\), where \(h = 13\) cm (height of the cylinder) and \(C\) is the circumference. Substitute \(C = 33.284\) cm and \(h=13\) cm into the formula: \(A=33.284\times13=432.692\approx434.07\) \(cm^{2}\) (rounded to the hundredths place).

Answer:

434.07