Water flows at a rate of 6000 cubic inches per minute into a cylindrical tank. The tank has a diameter of 180 inches and a height of 72 inches. What is the height, in inches, of the water in the tank after 5 minutes

The height of the water in the tank is 1.178 inches

Step-by-step explanation:

Since water flows at the rate of 6000 cubic inches per minute into a cylindrical tank, then after 5 minutes, "x" cubic inches of water must have flowed into the tank. To find x:

1minute 6000 cubic inches

5 minutes ?

Therefore, 5/1 × 6000 = 30,000 cubic inches (this is the volume of water that must have flown into the cylindrical tank.

Since π = 22/7

Radius = diameter/2 = 180/2 = 90inches

Height of the tank = 72 inches, then applying the formula for the volume of a cylinder(π×r×r×h):

22/7 × 90×90×72

12830400/7 = 1832914.29 cubic inches (This is the natural capacity of the tank).

It if after 5 minutes and 3000 cubic inches of water have flown into the cylindrical tank, then the height of the water in the tank =

(In this case, π =22/7, r=90, h= ?)

22/7 × 90×90×h = 30,000

178200/7 = 30,000

178200h = 210000

h = 210000/178200

h = 1.178 inches

alright so i think for this one it would to draw it out. this may be hard for me to try and draw, but i will do my best on here:

        r

  /       |     \

notice how it forms 2 triangles inside one bigger triangle.

so if we know the angle spr is the same as psr that is saying the measure of angle p is the same as angle s. this means the big triangle psr is either isosceles or equilateral. in both cases, the triangle is perfectly symmetrical when split down the middle, which is in this case rq. because we know it is perfectly symmetrical on both sides, we know that the two triangles inside the bigger one are equal.