Question

example 4: find the surface area of a round tank with a diameter of 30 ft. and a height of 15 ft. (do not include the top of the tank)

Explanation:

Step1: Calculate the radius

The radius \( r=\frac{d}{2}=\frac{30}{2} = 15\) ft.

Step2: Calculate the area of the bottom

The area of a circle \(A_{bottom}=\pi r^{2}\), substituting \(r = 15\), we get \(A_{bottom}=\pi\times15^{2}=225\pi\) square feet.

Step3: Calculate the lateral surface area

The lateral surface area of a cylinder \(A_{lateral}=2\pi r h\), substituting \(r = 15\) and \(h = 15\), we get \(A_{lateral}=2\pi\times15\times15 = 450\pi\) square feet.

Step4: Calculate the total surface area (excluding the top)

\(A = A_{bottom}+A_{lateral}=225\pi+450\pi=675\pi\)
Taking \(\pi\approx3.14\), \(A = 675\times3.14=2119.5\) square feet.

Answer:

\(2119.5\) square feet.