Please Help!! A septic tank has the shape shown in the figure. How many gallons does it hold? (1 cu ft = 7.48 gallons.) (Round to the nearest gallon)

The overall volume is the sum of the volume of a cylinder of height 5'9" and diameter 3'6", and a sphere of diameter 3'6" (two hemispheres = full sphere).

Volume of the cylinder = (area of the base) x (height) = pi * (diameter/2)^2 * 5.75ft = 3.1415 * (3.5ft/2)^2 * 5.75 ft = 55.32 ft^3

Volume of the sphere = 4/3 * pi * (3.5ft)^3 / 8 = 22.45 ft^3

Total volume = (Volume of cylinder) + (Volume of sphere) = (55.32 + 22.45) ft^3 = 77.77 ft^3

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tutorconsortium005 tutorconsortium005 · Answer 2 · 2022-06-12T10:49:35+02:00

The tank holds 641 gallons since the volume of the tank is 85.66 cubic feet. The tank has a cylindrical part and two hemispheres.

What is the volume of the cylinder?

The volume of the cylinder is V=Bh or V=2πrh.

Where B is the base area, h is the height of the cylinder and r is the radius.

What is the volume of the hemisphere?

The formula for the volume of a hemisphere: V = (2/3)πr³

Where r is the radius of the hemisphere.

Calculating the Volume of the septic tank:

The tank has a cylindrical part and two hemispheres.

So, the volume of the tank = (volume of the cylinder) +2 (volume of the hemisphere)

Finding the volume of the cylinder:

The height of the cylinder is h=5'9'' and the diameter is 3'6''.

(1 feet = 12 inches)

So, the diameter = 3 feet 6 inches = 3+(6/12) feet = 3.5 feet

Then, the radius r = 3.5/2 = 1.75 feet and

The height h=5 feet 9 inches = 5 + (9/12) feet = 5.75 feet

The volume of the cylinder = 2πrh

= 2π×1.75×5.75

= 63.22 cubic feet

Finding the volume of the hemisphere:

The diameter of the sphere is 3'6'' i.e., 3.5 feet

So, radius r = 1.75 feet

Then the volume of a hemisphere:

V = (2/3)πr³

= (2/3)π×(1.75)³

= 11.22 cubic feet

So,

The volume of the tank = (volume of the cylinder) +2 (volume of the hemisphere)

⇒ Volume of the tank = 63.22 + 2×11.22 =85.66 cubic feet.

Since it is given that for 1 cubic ft it holds 7.48 gallons then for 85.66 cubic ft it holds 85.66 × 7.48 = 640.73 gallons

Rounding to the nearest gallon. So, it holds 641 gallons.

Learn more about the volume of the cylinder here:

https://brainly.com/question/9554871

Learn more about the volume of the hemisphere here:

https://brainly.com/question/23242691

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