Question

find the surface area of a cylinder with a height of 8 yd and a base radius of 6 yd. use the value 3.14 for π, and do not do any rounding. be sure to include the correct unit.

Explanation:

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

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

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

We are given that \( r = 6 \) yd and \( h = 8 \) yd, and \( \pi = 3.14 \).

Step3: Calculate the area of the two circular bases

The area of one circular base is \( \pi r^2 \), so the area of two bases is \( 2\pi r^2 \). Substituting the values, we get:
\( 2\times3.14\times6^2 = 2\times3.14\times36 = 226.08 \) square yards.

Step4: Calculate the lateral (curved) surface area

The lateral surface area is \( 2\pi rh \). Substituting the values, we get:
\( 2\times3.14\times6\times8 = 301.44 \) square yards.

Step5: Add the areas of the two bases and the lateral surface area

The total surface area \( S = 226.08 + 301.44 = 527.52 \) square yards.

Answer:

\( 527.52 \) square yards (or \( 527.52 \, \text{yd}^2 \))