Question

a septic tank has the shape shown to the right. how many gallons does it hold? (1 ft³ = 7.48 gallons)
the tank holds gal (round to the nearest gallon as needed.)

Explanation:

Step1: Calculate the volume of the tank in cubic - feet

The septic tank can be thought of as a combination of a rectangular - prism and two half - cylinders (which together form a whole cylinder). The rectangular part has dimensions: length \(l = 6\) ft, width \(w=3\) ft, and height \(h = 3\) ft. The volume of the rectangular part \(V_{rect}=l\times w\times h=6\times3\times3 = 54\) \(ft^{3}\). The two semi - circles at the ends form a cylinder with diameter \(d = 3\) ft (so radius \(r=\frac{3}{2}=1.5\) ft) and length \(l = 6\) ft. The volume of the cylinder \(V_{cyl}=\pi r^{2}l=\pi\times(1.5)^{2}\times6=\pi\times2.25\times6 = 13.5\pi\approx13.5\times3.14 = 42.39\) \(ft^{3}\). The total volume of the tank \(V = V_{rect}+V_{cyl}=54 + 42.39=96.39\) \(ft^{3}\).

Step2: Convert the volume from cubic - feet to gallons

We know that \(1\) \(ft^{3}=7.48\) gallons. So the volume in gallons \(G=V\times7.48\). Substituting \(V = 96.39\) \(ft^{3}\), we get \(G=96.39\times7.48=96.39\times(7 + 0.48)=96.39\times7+96.39\times0.48=674.73+46.2672 = 720.9972\approx721\) gallons.

Answer:

721