To find the height of the right circular cylinder based on the given surface area, we first need to understand the formula for the surface area of a cylinder.
The surface area \( A \) of a right circular cylinder is given by: \[ A = 2\pi r(h + r) \] where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.
From the description, the diameter of the attached circles is 12 meters, so the radius \( r \) would be: \[ r = \frac{12}{2} = 6 \text{ meters} \]
Now, we can substitute the known values into the surface area equation: \[ 715.92 = 2 \pi (6)(h + 6) \]
Using \( \pi \approx 3.14 \): \[ 715.92 = 2 \times 3.14 \times 6 \times (h + 6) \] \[ 715.92 = 37.68 (h + 6) \]
Now, divide both sides by 37.68: \[ h + 6 = \frac{715.92}{37.68} \] \[ h + 6 \approx 19 \]
Now, subtract 6 from both sides: \[ h \approx 19 - 6 \] \[ h \approx 13 \]
Thus, the height of the cylinder is approximately 13 meters.
The correct response is: 13 meters.