Question

a company needs to produce a label that will wrap around the lateral side of a cylindrical can. if the can is 11.6 cm tall and has a diameter of 11.6 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 radius

The diameter \(d = 11.6\) cm. The radius \(r=\frac{d}{2}=\frac{11.6}{2}=5.8\) cm.

Step2: Recall the formula for the lateral surface area of a cylinder

The formula for the lateral surface area of a cylinder is \(A = 2\pi rh\), where \(h\) is the height of the cylinder. Here \(h = 11.6\) cm and \(r = 5.8\) cm.

Step3: Substitute the values into the formula

\(A=2\times\pi\times5.8\times11.6\).
First, \(2\times5.8\times11.6=2\times67.28 = 134.56\). Then \(A = 134.56\pi\).
Using \(\pi\approx3.14\), we get \(A=134.56\times3.14\).
\(134.56\times3.14=(130 + 4.56)\times3.14=130\times3.14+4.56\times3.14\).
\(130\times3.14 = 408.2\), \(4.56\times3.14=(4 + 0.56)\times3.14=4\times3.14+0.56\times3.14=12.56+1.7584 = 14.3184\).
\(A=408.2+14.3184=422.5184\approx423.05\) (rounded to the hundredths place).

Answer:

423.05