Answer:
The total weight of the water in a full tank, to the nearest pound is 3527 pounds per cubic foot
Step-by-step explanation:
Given:
Diameter of the hemispherical tank = 6 feet
Weight of water per cubic foot = 62. 4 pounds
To Find:
The total weight of the water in a full tank, to the nearest pound?
Solution:
We know that the volume of a sphere is:
[tex]V =\frac{4}{3}\pi r^3[/tex]
where
r = is the radius
In the question we are given with diameter,
So
[tex]radius = \frac{diameter}{2}[/tex]
radius = [tex]\frac{6}{2}[/tex]
Radius = 3
We need the volume of the hemisphere
So the volume of the hemisphere will be half of the volume of teh sphere
[tex]\frac{V}{2} = \frac{2}{3}\pi r^3[/tex]
Thus the volume of the hemisphere is
[tex]V =\frac{2}{3} \pi r^3[/tex]
Now substituting the values
[tex]V = \frac{2}{3} \pi(3)^3[/tex]
[tex]V = \frac{2}{3}\pi(27)[/tex]
[tex]V = \frac{54 \pi}{3}[/tex]
[tex]V = \frac{169.56}{2}[/tex]
V= 56.52 cubic foot
Now, the total weight of water of:
W = 56.52 x 62.4
W= 3526.848 pounds per cubic foot
To the nearest pounds
W= 3527 pounds per cubic foot
Answer:
3529
Step-by-step explanation:
If you are here from delta math this is the Answer
