Answer:
The total weight = 1286 × 62.4 = 80246 pounds.
Step-by-step explanation:
The formula of the volume of the sphere is
V = 4/3×π×r³
Given
d = 17 feet
as
d = 2r
so
r = d/2 = 17/2 = 8.5 feet
as
V = 4/3×π×r³
Since we need half of the volume as it is a hemispherical tank.
[tex]\frac{V}{2}=\pi r^3[/tex]
[tex]=\frac{2}{3}\times \:3.14\times \:8.5^3[/tex]
= 1286 ft³
Given that the weighs 62.4 pounds per cubic foot
Thus,
The total weight = 1286 × 62.4 = 80246 pounds.
The total weight of the water in a full hemispherical tank, which is filled with water, is 80,260 pounds.
The volume of the hemisphere is the amount of quantity, which is obtained by it in the 3 dimensional space.
The volume of the hemisphere can be calculated with the following formula.
[tex]V=\dfrac{2}{3}\pir^3[/tex]
Here, {r} is the radius of the hemisphere.
A hemispherical tank is filled with water and has a diameter of 17 feet. The radius of the hemisphere will be half of the diameter. Thus,
[tex]r=\dfrac{17}{2}\\r=8.5\rm\;ft[/tex]
The volume of the hemispherical tank is,
[tex]V=\dfrac{2}{3}\pi(8.5)^3\\V=1286.22\rm\; ft^3[/tex]
The water weighs 62.4 pounds per cubic foot. Thus, the total weight of the water in a full tank is,
[tex]W={1286.22}\times62.4\\W=80260\rm \;pounds[/tex]
Hence, the total weight of the water in a full hemispherical tank, which is filled with water, is 80,260 pounds.
Learn more about the volume of the hemisphere here;
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