Suppose you have a perfectly spherical water tank with an inside diameter of 8.6 metres. If the drain at the bottom of the tank can't handle a hydrostatic pressure of more than 50 kilopascals, what is the maximum volume of water, in litres, that can be contained in the tank? Assume that gravitational acceleration is exactly 9.81 m/s2.

The pressure is determined by the height of water in the tank.

P = rho g h
rho is about 1000 kg/m^3
g is 9.81
P is 50 *10^3 Pascals
solve for h in meters
then the radius of the tank is 4.3 meters and it is filled to depth h
volume of water = (1/6) pi h (3 rh^2 +h^2)
where rh is the radius at the water surface with depth h so rh = sqrt (2Rh-h^2)
then convert those m^3 to liters

Stop trying to cheat at neopets, it ruins it for the people who actually do the math.

296,1

To find the maximum volume of water that can be contained in the tank, we need to first determine the maximum height of the water column that will exert a pressure of 50 kilopascals (kPa) on the drain at the bottom.

The pressure exerted by a column of liquid is given by the equation:

P = ρgh

where P is the pressure, ρ is the density of the liquid, g is the gravitational acceleration, and h is the height of the column.

In this case, we need to solve for h. Rearranging the equation, we have:

h = P / (ρg)

The density of water is approximately 1000 kilograms per cubic meter, and the gravitational acceleration is given as 9.81 m/s^2. Plugging in these values, along with the given pressure of 50 kPa (which is equal to 50,000 Pa), we can calculate the maximum height:

h = 50,000 Pa / (1000 kg/m^3 * 9.81 m/s^2)
= 5.1 meters

Now that we have the maximum height of the water column, we can calculate the volume of the tank using the formula for the volume of a sphere:

V = (4/3) * π * r^3

The radius of the tank is half of the diameter, so the radius is 8.6 meters / 2 = 4.3 meters. Plugging in this value, we get:

V = (4/3) * π * (4.3 m)^3
= 319.7 cubic meters

Finally, we can convert the volume from cubic meters to liters by multiplying by 1000 (since there are 1000 liters in a cubic meter):

Maximum volume of water = 319.7 cubic meters * 1000 liters/cubic meter
= 319,700 liters

Therefore, the maximum volume of water that can be contained in the tank is 319,700 liters.