defazajx

2021-01-02

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?

Layton

Skilled2021-01-03Added 89 answers

The formula for calculating a cylinder's surface area $S=2\pi {r}^{2}+2\pi rh$ where h is the cylinder's height and r is the radius of the circular base.

Since the diameter of the tank is $d=36$ ft, then the radius $r=d\xf72=36\xf72=18ft$.

Since we know the surface area is $S=4750.1f{t}^{2}$ and the radius is r=18, In order to solve for h, we can then enter these values into the surface area formula as follows:

$S=2\pi {r}^{2}+2\pi \text{}rh\text{}\text{Surface are formula.}$

$4750.1=2\pi (18{)}^{2}+2\pi (18)h\text{}\text{Substitute S}=4750.1\text{}and\text{}r=18.$ $4750.1=2\pi (324)+36\pi h\text{}\text{Simplify.}$ $4750.1=648\pi +36\pi h\text{}\text{Simplify.}$ $4750.1-648\pi =36\pi \text{}Substract\text{}648\pi \text{}on\text{}both\text{}sides.$ $(4750.1-648\pi )/(36\pi )=h\text{}Divide\text{}both\text{}sides\text{}by\text{}36\pi .$ $24\approx h\text{}\text{Evaluate using a calculator.}$ The height of the cylinder is then 24 ft.

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