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 731.05 gal (round to the nearest gallon as needed.)

Explanation:

Step1: Identify the shape components

The septic - tank can be considered as a combination of a rectangular - prism part and two semi - circles (which form a full circle) at the ends. The dimensions seem to be a length of \(l = 5\) ft and a diameter of \(d=4\) ft (so radius \(r = 2\) ft).

Step2: Calculate the volume of the cylindrical part (formed by the two semi - circles and the length)

The volume of a cylinder is \(V=\pi r^{2}h\). Here, \(r = 2\) ft and \(h = 5\) ft. So \(V=\pi\times(2)^{2}\times5=20\pi\approx20\times3.14 = 62.8\) \(ft^{3}\).

Step3: Convert the volume from cubic feet to gallons

We know that \(1\ ft^{3}\approx7.48\) gallons. So the volume in gallons \(V_{g}=62.8\times7.48\approx470.744\). But we made a wrong assumption above. Let's assume the correct dimensions are: if we consider the tank as a rectangular prism with two semi - circular ends. The length of the rectangular part \(l = 5\) ft, width \(w=4\) ft and height \(h = 6\) ft.
The volume of the rectangular part \(V_{1}=l\times w\times h=5\times4\times6 = 120\) \(ft^{3}\).
The two semi - circles at the ends form a circle with radius \(r = 2\) ft. The volume of the circular - part (cylindrical part) \(V_{2}=\pi r^{2}l=\pi\times(2)^{2}\times5=20\pi\approx62.8\) \(ft^{3}\).
The total volume \(V = V_{1}+V_{2}=120 + 62.8=182.8\) \(ft^{3}\).
Converting to gallons: \(V_{total}=182.8\times7.48=182.8\times(7 + 0.48)=182.8\times7+182.8\times0.48=1279.6+87.744 = 1367.344\approx1367\) gallons.

Answer:

1367