Final answer:
To find the length of the prism, we can use the volume of the displaced water when the prism is submerged, which is equal to the volume of the prism. The base area of the tank multiplied by the water level rise (2 cm) gives the volume of displaced water. Dividing this volume by the prism's cross-sectional area provides the prism's length.
Step-by-step explanation:
To calculate the length of the prism, we need to understand the relationship between the water level rise and the volume of the prism. When the prism is lowered into the tank, the water level rises due to the displacement of water equivalent to the volume of the submersed part of the prism. Given that the water level rises by 2 cm, we can find the volume of the displaced water, which is the same as the volume of the prism.
Assuming the base area (A) of the tank is known, we use the formula for the volume of a cuboid (V = A × height) to calculate the volume of water displaced (ΔV), where the height increase is 2 cm:
ΔV = A × 2 cm
We can then equate the volume of the prism (V_prism) to ΔV since they are equal. If the cross-sectional area of the prism (A_prism) is known, the length of the prism (L) can be found by rearranging the formula for the volume of a prism (V_prism = A_prism × L):
L = ΔV / A_prism
Without the specifics of the base area of the tank or the cross-sectional area of the prism, we cannot provide a numerical answer but this is the method that would be used to calculate the length of the prism.