Question

unit 7 cones, cylinders, & spheres → lesson 3 surface area of cylinders 8 yd. find the surface area of the cylinder. use the approximation 3.14 for pi.

Explanation:

Step1: Find the radius

Assume the diameter of the base is \(d = 10\) yd (since the length from one end to the other on the top is not clear, but common in such problems, if we assume the top - to - top length (diameter) is \(10\) yd). Then the radius \(r=\frac{d}{2}=\frac{10}{2} = 5\) yd.

Step2: Calculate the area of the base

The formula for the area of a circle is \(A_{base}=\pi r^{2}\). Substituting \(r = 5\) yd and \(\pi=3.14\), we get \(A_{base}=3.14\times5^{2}=3.14\times25 = 78.5\) \(yd^{2}\).

Step3: Calculate the lateral surface area

The formula for the lateral surface area of a cylinder is \(A_{lateral}=2\pi r h\). Substituting \(r = 5\) yd, \(h = 8\) yd and \(\pi = 3.14\), we have \(A_{lateral}=2\times3.14\times5\times8=3.14\times80=251.2\) \(yd^{2}\).

Step4: Calculate the total surface area (assuming one base, since the top is open)

The formula for the surface area of the open - top cylinder is \(A=A_{base}+A_{lateral}\). Substituting the values from Step 2 and Step 3, \(A = 78.5+251.2=329.7\) \(yd^{2}\).

Answer:

\(329.7\) \(yd^{2}\)