Question

unit 7 cones, cylinders, & spheres > lesson 3 surface area of cylinders 3 yd. find the surface area of the cylinder. use the approximation of 3.14 for pi.

Explanation:

Step1: Find the radius

The diameter is \(d = 4\) yd (assuming from the visual, as it's not explicitly stated but standard in such problems). The radius \(r=\frac{d}{2}=\frac{4}{2} = 2\) yd.

Step2: Calculate the lateral surface area

The formula for the lateral surface area of a cylinder \(A_{l}=2\pi rh\). Substitute \(r = 2\) yd, \(h=3\) yd, \(\pi = 3.14\).
\(A_{l}=2\times3.14\times2\times3\)
\(A_{l}=37.68\) \(yd^{2}\)

Step3: Calculate the area of the base

The formula for the area of a circle \(A_{b}=\pi r^{2}\). Substitute \(r = 2\) yd, \(\pi=3.14\).
\(A_{b}=3.14\times2^{2}=3.14\times4 = 12.56\) \(yd^{2}\)

Step4: Calculate the total surface area (since it's an open - top cylinder, \(A = A_{l}+A_{b}\))

\(A=37.68 + 12.56=50.24\) \(yd^{2}\)

Answer:

\(50.24\) square yards