A rectangular water tank of length 60 cm and width 40 cm contains water up to depth of 30 cm. A peice of ice measuring 20 cm by 15 cm by 12 cm is dropped into the tank of water. Calculate the new depth of water when the ice melts completely, assuming its volume decreases by 1/10.
the ice's volume is 20*15*12 = 3600 cm^3
melted, the volume is 3600-360 = 3240 cm^3
The area of the water is 2400 cm^3
That means the water level will rise by 3240/2400 = 1.35 cm
...
To calculate the new depth of water when the ice melts completely, we need to calculate the volume of water displaced by the ice and subtract it from the initial depth.
First, let's find the volume of the water tank:
Volume of the water tank = length * width * depth = 60 cm * 40 cm * 30 cm = 72,000 cm³
Next, let's find the volume of the ice:
Volume of the ice = length * width * depth = 20 cm * 15 cm * 12 cm = 3,600 cm³
Now, let's calculate the volume of water displaced by the ice:
Volume of water displaced = Volume of the ice
Since the volume of the ice decreases by 1/10 after it melts, the new volume of the ice will be (9/10) * Volume of the ice:
New volume of the ice = (9/10) * 3,600 cm³ = 3,240 cm³
Therefore, the volume of water displaced by the ice is 3,240 cm³.
Finally, let's calculate the new depth of water:
New depth of water = initial depth - (volume of water displaced / (length * width))
New depth of water = 30 cm - (3,240 cm³ / (60 cm * 40 cm))
New depth of water = 30 cm - (3,240 cm³ / 2400 cm²)
New depth of water = 30 cm - 1.35 cm
New depth of water = 28.65 cm
Therefore, the new depth of water when the ice melts completely is 28.65 cm.