Question

a cylinder has a diameter of 6 cm and a height of 3 cm. what is the surface area of the cylinder? enter your answer, in exact form, in the box. cm²

Explanation:

Step1: Find the radius

The formula for the radius \(r\) of a circle is \(r=\frac{d}{2}\), where \(d\) is the diameter. Given \(d = 6\) cm, so \(r=\frac{6}{2}=3\) cm.

Step2: Recall the surface - area formula for a cylinder

The surface - area formula for a cylinder is \(S = 2\pi r(r + h)\), where \(r\) is the radius and \(h\) is the height. Here, \(r = 3\) cm and \(h=3\) cm.

Step3: Substitute the values into the formula

Substitute \(r = 3\) and \(h = 3\) into \(S=2\pi r(r + h)\). Then \(S=2\pi\times3\times(3 + 3)\).
First, calculate the sum inside the parentheses: \(3+3 = 6\).
Then, multiply: \(2\pi\times3\times6=36\pi\).

Answer:

\(36\pi\)