Question

what is the surface area of a cylinder with base radius 3 and height 8? either enter an exact answer in terms of \\(\pi\\) or use 3.14 for \\(\pi\\) and enter your answer as a decimal. image of a cylinder with radius 3 and height 8 square units

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 of the base and \( h \) is the height of the cylinder.

Step2: Substitute the given values of \( r \) and \( h \)

We are given that \( r = 3 \) and \( h = 8 \). Substituting these values into the formula, we get:
\( S=2\pi(3)^2 + 2\pi(3)(8) \)

Step3: Simplify the expression

First, calculate \( (3)^2=9 \). Then:
\( S = 2\pi\times9+2\pi\times3\times8 \)
\( S=18\pi + 48\pi \)
\( S=(18 + 48)\pi \)
\( S = 66\pi \)

If we use \( \pi\approx3.14 \):
\( S=66\times3.14 \)
\( S = 207.24 \)

Answer:

If we want the exact answer in terms of \( \pi \), the surface area is \( 66\pi \) square units. If we use \( 3.14 \) for \( \pi \), the surface area is \( 207.24 \) square units.