Question

A closed cylindrical tank contains 36pi cubic feet of water and is filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?(A) 2(B) 3(C) 4(D) 6(E) 9

Answer 1

Answer:

2.12 ft above ground level

Step-by-step explanation:

Volume of the cylindrical tank is 36*π

Tank is filled to half its capacity, that means tank is filled 18*π, and level of water is 4 feet, then the height of the cylinder is 8 feet

With the above information we can calculate the radius of the base of the cylinder, according to

V  =  36*π  = π*r²*h     ⇒  36 = r²*h     ⇒   36/8 = r²    ⇒  r = 2.12 ft

Then the radius of the base is  2.12 ft

When the cylindrical tank is place on its side, the level of water inside have to be 2.12 ft above ground level. That is the level of half its capacity

Answer 2

Answer:

h=3ft

Step-by-step explanation:

In order to solve this problem, we can start by drawing a diagram of the situation, which will help us visualize theh problem better (see attached picture).

So the idea here is to use the given volume of water to find the radius of the cylinder. We know that the volume of a cylinder is given by the formula:

$V_{cylinder}=\pi r^{2}h$

so we can go ahead and solve the formula for the radius r, so we get:

$r^{2}=\frac{V_{cylinder}}{\pi h}$

and

$r=\sqrt{\frac{V_{cylinder}}{\pi h}}$

so we can now substitute the data given by the problem, so we get:

$r=\sqrt{\frac{36\pi ft^{3}}{4\pi ft}}$

Which yields:

r=3ft

When the tank is placed on its side, you may see that its height is given by the diameter of the cylinder. If the cylinder is half full, this means that the height of the water will be its radius, so the height of the cylinder is 3ft.