By how much will the level of the water rise?

Question

The rectangular prism is placed in a cylindrical tank of water. If the area of the base of the cylinder is 25.5cm^2, by how much will the level of the water rise?

 

 

Answer 1

Let V_p be the volume of the rectangular prism and V_w be the volume of the water within the cylindrical tank.  Suppose the water is initially at height h₁:

 

V_w = (Area of the Base)*(height) = (25.5)*h₁

 

When you add the prism (assuming it's denser than the water and fully submerges), you increase the volume of the water by the volume of the prism.  Let h₂ be the new height of the water after the prism is added:

 

V_w = (25.5)*h₂ = (25.5)*h₁ + V_p

 

h₂ = h₁ + (V_p/25.5)

h₂ - h₁ = V_p/25.5     (This is the amount that the water level rises)

 

You didn't state what the volume of the prism (V_p) is, so I can't compute a numerical answer.  If the problem gives you the volume of the prism, just plug it in to the orange formula above to get the numerical answer.