Surface Area of a Cylinder with Water

Medium Functions And Modeling Modeling With Geometry

A cylindrical water tank has a radius of 5 meters and a height of 10 meters. The tank is filled with water to a height of 6 meters. The surface area of the cylinder that contains the water can be calculated using the formula:

$$SA = 2egin{pmatrix} ext{base area} + ext{lateral area} \\ ext{base area} = ext{circle area} = ext{radius}^2 imes ext{π} \\ ext{lateral area} = ext{circumference} imes ext{height} \\ ext{circumference} = 2 ext{π} imes ext{radius} \\ ext{height} = ext{varies with water level} \\ ext{we calculate for } h = 6 ext{m} ext{ (water height)} ext{ where base area is considered only 1 time} \\ SA = 2 ext{π}r^2 + 2 ext{π}rh $$

If π is approximated as 3.14, what is the surface area of the exposed water surface when the tank is filled to this height?

$$114.0 ext{ m}^2$$

$$141.6 ext{ m}^2$$

$$157.0 ext{ m}^2$$

$$471.0 ext{ m}^2$$

Hint

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