A rectangular tank of 5 m long,4 m wide and 5 m high is filled with water to a depth 3 m. If a robot of volume 20 cubic metre is added to the tank, how much will the water level rise?
Assuming the robot is completely submerged, then the water will rise by
(20m^3)/(5m*4m) = 1m
Doesn't really matter how tall the tank is, or how much water is already there, as long as the entire volume of the robot is submerged.
To find out how much the water level will rise when the robot is added to the tank, we need to calculate the volume of the robot and then compare it to the change in volume of water.
Given information:
Length of the tank (L) = 5 m
Width of the tank (W) = 4 m
Height of the tank (H) = 5 m
Initial depth of water (D1) = 3 m
Volume of the robot (V_robot) = 20 cubic meters
Based on the given dimensions, we can find the initial volume of water in the tank using the formula for the volume of a rectangular solid:
V_initial_water = L * W * D1
= 5 m * 4 m * 3 m
= 60 cubic meters
Now, we can add the volume of the robot to the initial volume of water to find the final volume of water after the robot is added:
V_final_water = V_initial_water + V_robot
= 60 cubic meters + 20 cubic meters
= 80 cubic meters
Since the water level rises when the volume of water increases, the change in volume of water is:
ΔV_water = V_final_water - V_initial_water
= 80 cubic meters - 60 cubic meters
= 20 cubic meters
Therefore, the water level will rise by 20 cubic meters when the robot is added to the tank.