Question

given that the r = 6 m and the h = 7 m, find the surface area of the cylinder, rounded to the nearest hundredth. use \\( \pi \approx 3.14 \\) in all calculations:
\\( \text{m}^2 \\)

Explanation:

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

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

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

We know that \( r = 6 \) m, \( h = 7 \) m, and \( \pi \approx 3.14 \). First, calculate the area of the two circular bases (\( 2\pi r^2 \)):

$$ 2 \times 3.14 \times 6^2 = 2 \times 3.14 \times 36 = 226.08 $$

Next, calculate the lateral (curved) surface area (\( 2\pi rh \)):

$$ 2 \times 3.14 \times 6 \times 7 = 263.76 $$

Step3: Add the two areas together to get the total surface area

$$ SA = 226.08 + 263.76 = 489.84 $$

Answer:

The surface area of the cylinder is \( 489.84 \) square meters.