Question

the surface area of this cylinder is 4,114.656 square meters. what is the height? round your answer to the nearest hundredth. $h \approx$ $square$ meters

Explanation:

Step1: Recall total surface area formula

The total surface area \( S \) of a cylinder is \( S = 2\pi r^2 + 2\pi r h \), where \( r = 18 \, \text{m} \), \( S = 4114.656 \, \text{m}^2 \).

Step2: Calculate area of two circular bases

First compute \( 2\pi r^2 \):
\( 2 \times \pi \times 18^2 = 2 \times \pi \times 324 = 648\pi \approx 648 \times 3.1416 = 2035.752 \)

Step3: Isolate lateral surface area

Subtract base area from total surface area:
\( 2\pi r h = S - 2\pi r^2 = 4114.656 - 2035.752 = 2078.904 \)

Step4: Solve for height \( h \)

Rearrange to solve for \( h \):
\( h = \frac{2078.904}{2\pi r} = \frac{2078.904}{2 \times 3.1416 \times 18} = \frac{2078.904}{113.0976} \approx 18.38 \)

Answer:

\( h \approx 18.38 \) meters