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:
![V =\frac{4}{3}\pi r^3](https://tex.z-dn.net/?f=V%20%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3)
where
r
= is the radius
In the question we are given with diameter,
So
![radius = \frac{diameter}{2}](https://tex.z-dn.net/?f=radius%20%20%3D%20%5Cfrac%7Bdiameter%7D%7B2%7D)
radius = ![\frac{6}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B2%7D)
Radius = 3
We need the volume of the hemisphere
So the volume of the hemisphere will be half of the volume of teh sphere
![\frac{V}{2} = \frac{2}{3}\pi r^3](https://tex.z-dn.net/?f=%5Cfrac%7BV%7D%7B2%7D%20%3D%20%5Cfrac%7B2%7D%7B3%7D%5Cpi%20r%5E3)
Thus the volume of the hemisphere is
![V =\frac{2}{3} \pi r^3](https://tex.z-dn.net/?f=V%20%3D%5Cfrac%7B2%7D%7B3%7D%20%5Cpi%20r%5E3)
Now substituting the values
![V = \frac{2}{3} \pi(3)^3](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B2%7D%7B3%7D%20%5Cpi%283%29%5E3)
![V = \frac{2}{3}\pi(27)](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B2%7D%7B3%7D%5Cpi%2827%29)
![V = \frac{54 \pi}{3}](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B54%20%5Cpi%7D%7B3%7D)
![V = \frac{169.56}{2}](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B169.56%7D%7B2%7D)
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