Question

1. find the surface area. round your answer to the nearest hundredth.

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 \( h \)

From the diagram, the radius \( r = 9 \) and the height \( h = 18 \).

Step3: Calculate the two parts of the formula separately

First, calculate \( 2\pi r^2 \):
\( 2\pi r^2 = 2\times\pi\times9^2 = 2\times\pi\times81 = 162\pi \)

Second, calculate \( 2\pi rh \):
\( 2\pi rh = 2\times\pi\times9\times18 = 324\pi \)

Step4: Add the two parts together

\( S = 162\pi + 324\pi = 486\pi \)

Step5: Compute the numerical value and round to the nearest hundredth

Using \( \pi \approx 3.14159 \), we have:
\( S \approx 486\times3.14159 \approx 1526.81 \) (rounded to the nearest hundredth)

Answer:

The surface area of the cylinder is approximately \(\boxed{1526.81}\).