a septic tank has the shape shown to the right. how many gallons does it hold? (1 ft³ ≈ 7.48 gallons) the…

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.)

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.)

Answer

Explanation:

Step1: Convert dimensions to feet

First, convert 5' 6" and 3' 9" to feet. 6 inches = 6/12 = 0.5 feet, so 5' 6" = 5.5 feet. 9 inches = 9/12 = 0.75 feet, so 3' 9" = 3.75 feet.

Step2: Calculate the volume of the tank

The tank can be thought of as a cylinder with two - semi - circles (which form a full circle) at the ends. The formula for the volume of a cylinder is $V=\pi r^{2}h$. The radius $r=\frac{3.75}{2}$ feet and the length $h = 5.5$ feet. So $V=\pi\times(\frac{3.75}{2})^{2}\times5.5=\pi\times\frac{14.0625}{4}\times5.5=\frac{77.34375\pi}{4}\approx\frac{77.34375\times3.14}{4}=\frac{242.859375}{4}=60.71484375$ cubic feet.

Step3: Convert volume to gallons

Since 1 cubic foot is approximately 7.48 gallons, the volume in gallons is $V_{gal}=60.71484375\times7.48 = 60.71484375\times\frac{748}{100}=60.71484375\times7.48 = 454.1470313$ gallons.

Step4: Round the result

Rounding 454.1470313 to the nearest gallon gives 454 gallons.

Answer:

454