Question

a cylindrical soda can has a volume of 108π cubic centimeters (cm³) and a height of 12 cm. what is the surface area of the soda can in square centimeters? choose 1 answer: a 18π cm² b 36π cm² c 72π cm² d 90π cm²

Explanation:

Step1: Find the radius of the cylinder

The volume formula of a cylinder is \(V=\pi r^{2}h\). Given \(V = 108\pi\) and \(h=12\), substitute into the formula:
\(108\pi=\pi r^{2}\times12\).
Divide both sides by \(12\pi\): \(r^{2}=\frac{108\pi}{12\pi}=9\).
Take the square root of both sides: \(r = 3\) (since \(r>0\)).

Step2: Calculate the surface area of the cylinder

The surface area formula of a cylinder is \(S = 2\pi r^{2}+2\pi rh\).
Substitute \(r = 3\) and \(h=12\) into the formula:
\(S=2\pi\times3^{2}+2\pi\times3\times12\).
First, calculate \(2\pi\times3^{2}=2\pi\times9 = 18\pi\).
Second, calculate \(2\pi\times3\times12=72\pi\).
Then, \(S=18\pi + 72\pi=90\pi\).

Answer:

D. \(90\pi\mathrm{cm}^{2}\)