A tank is full of water. Find the work W required to pump the water out of the spout.
r=6
h=3
is this a spherical or cylindrical tank?
To find the work required to pump the water out of the spout, we can use the formula:
W = mgh
where:
W is the work
m is the mass of the water
g is the acceleration due to gravity
h is the height from which the water is being pumped
In this case, we need to find the mass of the water. We can do this by using the formula for the volume of a cylinder:
V = πr^2h
where:
V is the volume
r is the radius of the base of the cylinder
h is the height of the cylinder
Given that r = 6 and h = 3, we can substitute these values into the formula to find the volume:
V = π(6^2)(3)
V = π(36)(3)
V = 108π
Now, we can use the volume to find the mass of the water. The density of water is approximately 1000 kg/m^3. We can use this value to find the mass:
m = ρV
where:
m is the mass
ρ is the density
V is the volume
Substituting the values, we get:
m = 1000 * 108π
Now, we have the mass (m) and the height (h) values, so we can finally calculate the work required (W):
W = mgh
Substituting the values, we get:
W = (1000 * 108π) * 9.8 * 3
Calculating this expression will give us the final answer for the work required to pump the water out of the spout.