Question

find the lateral surface area of the cylinder given the height and radius shown. note that the figure is not to scale.

Explanation:

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

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

Step2: Identify the values of \(r\) and \(h\)

From the problem, \(r = 17\) and \(h=20\).

Step3: Substitute the values into the formula

Substitute \(r = 17\) and \(h = 20\) into \(S=2\pi rh\). We get \(S=2\pi\times17\times20\).

Step4: Calculate the result

First, calculate \(2\times17\times20= 680\). So, \(S = 680\pi\).

Answer:

$680\pi$