To find the height of the right circular cylinder, let's first determine the dimensions involved.
-
Diameter of the circles: Given that the diameter of each circle is 12 meters, the radius (r) will be: \[ r = \frac{12}{2} = 6 \text{ meters} \]
-
Surface Area of a Cylinder: The surface area (SA) of a right circular cylinder is given by the formula: \[ SA = 2\pi r(h + r) \] where \( h \) is the height of the cylinder.
-
Given Surface Area: We know that the surface area is 715.92 square meters. Using \( \pi \approx 3.14 \), we can plug in the values into the formula: \[ 715.92 = 2 \times 3.14 \times 6 (h + 6) \] Simplifying the equation: \[ 715.92 = 2 \times 3.14 \times 6 \times (h + 6) \] \[ 715.92 = 37.68 (h + 6) \]
-
Solving for \( h + 6 \): \[ h + 6 = \frac{715.92}{37.68} \approx 19 \]
-
Finding \( h \): \[ h = 19 - 6 = 13 \text{ meters} \]
Therefore, the height of the cylinder is 13 meters.
The correct response is: 13 meters.