Question

what is the lateral area of the cylinder? 9 ft 22 ft a) 615.85 ft.² b) 625.25 ft.² c) 515.01 ft.² d) 622.04 ft.²

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 \(d = 22\) ft, so the radius \(r=\frac{d}{2}=\frac{22}{2}=11\) ft, and the height \(h = 9\) ft.

Step2: Substitute the values into the formula

Substitute \(r = 11\) and \(h=9\) into \(L = 2\pi rh\). Then \(L=2\times\pi\times11\times9\).
First, calculate \(2\times11\times9 = 198\). So \(L = 198\pi\).
Using \(\pi\approx3.1416\), then \(L\approx198\times3.1416\).
\(198\times3.1416=(200 - 2)\times3.1416=200\times3.1416-2\times3.1416\).
\(200\times3.1416 = 628.32\) and \(2\times3.1416=6.2832\).
\(L\approx628.32-6.2832 = 622.0368\approx622.04\)

Answer:

D. \(622.04\space ft^{2}\)