# Water is stored in a cylindrical tank with a diameter of 36 feet. The surface area of the tank is 4750.1 square feet. What is the height of the tank?

Question
Solid Geometry
Water is stored in a cylindrical tank with a diameter of 36 feet. The surface area of the tank is 4750.1 square feet. What is the height of the tank?

2021-01-03

The surface area of a cylinder is given by the formula $$S= 2\pi r^{2}+2\pi rh$$ where r is the radius of the circular base and h is the height of the cylinder.
Since the diameter of the tank is $$d=36$$ ft, then the radius $$r=d\div2=36\div2=18 ft$$.
Since we know the surface area is $$S=4750.1 ft^{2}$$ and the radius is r=18, we can then substitute these values into the surface area formula to solve for h:
$$S= 2\pi r^{2}+2\pi\ rh\ \text{Surface are formula.}$$
$$4750.1= 2\pi(18)^{2}+2\pi(18)h\ \text{Substitute S}= 4750.1\ and\ r=18.$$ $$4750.1= 2\pi(324)+36\pi h\ \text{Simplify.}$$ $$4750.1= 648\pi+36\pi h\ \text{Simplify.}$$ $$4750.1-648\pi= 36\pi \ \text{Substract 648pi on both sides.}$$ $$(4750.1-648\pi)/(36\pi)=h\ \text{Divide both sides by 36pi.}$$ $$24\approx h\ \text{Evaluate using a calculator.}$$ The height of the cylinder is then 24 ft.

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