Question

1. an oil storage tank in the shape of a right circular cylinder has a volume of 55 gallons. write an equation in terms of the radius, r, that represents the surface area a(r). note that the tank will have both a top and bottom to seal the container when filled with oil.

Explanation:

Step1: Recall the volume formula for a cylinder

The volume formula for a right - circular cylinder is \(V=\pi r^{2}h\). Given \(V = 55\) gallons, so \(55=\pi r^{2}h\). Solve for \(h\): \(h=\frac{55}{\pi r^{2}}\).

Step2: Recall the surface area formula for a closed - top cylinder

The surface area formula for a closed - top cylinder is \(A(r)=2\pi r^{2}+2\pi rh\).

Step3: Substitute \(h\) into the surface area formula

Substitute \(h = \frac{55}{\pi r^{2}}\) into \(A(r)\):

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Answer:

\(A(r)=2\pi r^{2}+\frac{110}{r}\)