Question

geometry
which equation can be used to find the surface area of the cylinder?
$s = 2\pi(6)^{2}+2\pi(6)(14)$
$s = 2(3)^{2}+2(3)(14)$
$s = 2\pi(14)^{2}+2\pi(14)(6)$
$s = 2\pi(3)^{2}+2\pi(3)(14)$

Explanation:

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

The formula for the surface area 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 from the diameter

Given \( d = 6\) cm, the radius \( r=\frac{d}{2}=\frac{6}{2}=3\) cm.

Step3: Substitute \( r = 3\) cm and \( h = 14\) cm 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)