Question

which equation can be used to find the surface area of the cylinder?

$s = 2\pi(6)^{2}+2\pi(6)(14)$

$s = 2(3)^{2}+2(3)(14)$

$s = 2\pi(14)^{2}+2\pi(14)($

$s = 2\pi(3)^{2}+2\pi(3)(14)$

Explanation:

Step1: Recall the formula for the surface area of a cylinder

The surface area formula of a cylinder is \(S = 2\pi r^{2}+2\pi rh\), where \(r\) is the radius and \(h\) is the height.

Step2: Find the radius

Given the diameter \(d = 6\space cm\), the radius \(r=\frac{d}{2}=\frac{6}{2}=3\space cm\), and the height \(h = 14\space cm\).

Step3: Substitute \(r = 3\) and \(h = 14\) into the formula

Substituting into \(S = 2\pi r^{2}+2\pi rh\), we get \(S=2\pi(3)^{2}+2\pi(3)(14)\).

Answer:

\(S = 2\pi(3)^{2}+2\pi(3)(14)\) (the fourth option in the original problem layout)