Question

a company needs to produce a label that will wrap around the lateral side of a cylindrical can. if the can is 18 cm tall and has a diameter of 12 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 \( d = 12\) cm, so \( C=\pi\times12=12\pi\) cm.

Step2: Calculate the lateral - surface area

The formula for the lateral - surface area of a cylinder is \( A = Ch\) (where \(C\) is the circumference of the base and \(h\) is the height of the cylinder). Given \(h = 18\) cm and \(C = 12\pi\) cm. Then \(A=12\pi\times18=216\pi\) cm².

Step3: Substitute the value of \(\pi\) and round

Substitute \(\pi\approx3.14159\). Then \(A = 216\times3.14159=678.58344\approx678.58\) cm².

Answer:

\( 678.58 \)