Question

4 a lipstick container has a diameter of 12 millimeters (mm) and a height of 60 mm. what is the surface area of the lipstick container? round your answer to the nearest square millimeter.

Explanation:

Step1: Find the radius

The formula for radius \(r\) is \(r=\frac{d}{2}\), where \(d\) is the diameter. Given \(d = 12\) mm, so \(r=\frac{12}{2}=6\) mm.

Step2: Recall the surface - area formula for a cylinder

The surface - area formula for a cylinder is \(S = 2\pi r^{2}+2\pi rh\).

Step3: Substitute the values of \(r\) and \(h\) into the formula

We know \(r = 6\) mm and \(h=60\) mm.
First, calculate \(2\pi r^{2}\):
\(2\pi r^{2}=2\times\pi\times6^{2}=2\times\pi\times36 = 72\pi\)
Second, calculate \(2\pi rh\):
\(2\pi rh=2\times\pi\times6\times60=720\pi\)
Then, \(S=72\pi + 720\pi=(72 + 720)\pi=792\pi\)

Step4: Calculate the numerical value

Using \(\pi\approx3.14\), we have \(S\approx792\times3.14 = 2486.88\approx2487\) \(mm^{2}\)

Answer:

\(2487\) \(mm^{2}\)