The height of water in tank after 5 minutes is 1.2 inches
Solution:
Water flows at a rate of 6000 cubic inches per minute into a cylindrical tank
Therefore,
1 minute = 6000 cubic inches
Therefore, for 5 minutes, rate is given as:
5 minute = 5 x 6000 = 30000 cubic inches
The tank has a diameter of 180 inches and a height of 72 inches
Diameter = 180 inches
[tex]Radius = \frac{diameter}{2} = \frac{180}{2} = 90[/tex]
Thus, radius = 90 inches
We know that, volume of the water filled in the cylindrical tank in 5 minutes is 30000 cubic inches
Volume of cylinder is given as:
[tex]v = \pi r^2 h[/tex]
Where, "r" is the radius and "h" is the height of tank
[tex]30000 = 3.14 \times (90)^2 \times h\\\\30000 = 25434 \times h\\\\h = \frac{30000}{25434}\\\\h = 1.179 \approx 1.2[/tex]
Thus height of water in tank after 5 minutes is 1.2 inches
