Question

find the lateral area of the cylinder. round to the nearest hundredth if necessary, do not include units with your answer.

Explanation:

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

The formula for the lateral area \(L\) of a cylinder is \(L = 2\pi rh\), where \(r\) is the radius and \(h\) is the height. Given the diameter \(d = 26\) in, the radius \(r=\frac{d}{2}=\frac{26}{2}=13\) in, and the height \(h = 17\) in.

Step2: Substitute the values into the formula

Substitute \(r = 13\) and \(h = 17\) into \(L = 2\pi rh\). So \(L=2\pi\times13\times17\).

Step3: Calculate the value

First, calculate \(2\times13\times17=442\). Then \(L = 442\pi\). Using \(\pi\approx3.14159\), we have \(L\approx442\times3.14159\).
\(442\times3.14159=(400 + 40+ 2)\times3.14159=400\times3.14159+40\times3.14159+2\times3.14159\)
\(=1256.636+125.6636 + 6.28318\approx1388.58\)

Answer:

1388.58