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 \(r\) is half of the diameter. Given \(d = 30\) ft, so \(r=\frac{d}{2}=\frac{30}{2}=15\) ft.

Step2: Find the area of the base

The area of a circle (base of the tank) is \(A_{base}=\pi r^{2}\). Substituting \(r = 15\) ft, we get \(A_{base}=\pi\times(15)^{2}=225\pi\) square - feet.

Step3: Find the lateral surface area

The formula for the lateral surface area of a cylinder is \(A_{lateral}=2\pi r h\). Substituting \(r = 15\) ft and \(h = 15\) ft, we have \(A_{lateral}=2\pi\times15\times15 = 450\pi\) square - feet.

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

The total surface area \(A=A_{base}+A_{lateral}\). Substituting the values of \(A_{base}\) and \(A_{lateral}\), we get \(A = 225\pi+450\pi=675\pi\). Using \(\pi\approx3.14\), \(A\approx675\times3.14 = 2119.5\) square - feet.

Answer:

The surface area of the round tank (excluding the top) is approximately \(2119.5\) square - feet.