You can find the volume of an irregularly shaped solid object by completely submerging it in water and calculating the volume of water the object displaces. You completely submerge a solid object in a rectangular tank that has a base 40 centimeters40 centimeters by 30 centimeters30 centimeters and is filled with water to a depth of 20 centimeters.20 centimeters. The object sinks to the bottom, and the water level goes up 0.25 centimeters.0.25 centimeters. What is the volume, in cubic centimeters, of the object?
Question
You can find the volume of an irregularly shaped solid object by completely submerging it in water and calculating the volume of water the object displaces. You completely submerge a solid object in a rectangular tank that has a base 40 centimeters40 centimeters by 30 centimeters30 centimeters and is filled with water to a depth of 20 centimeters.20 centimeters. The object sinks to the bottom, and the water level goes up 0.25 centimeters.0.25 centimeters. What is the volume, in cubic centimeters, of the object?
Solution
To find the volume of the object, we need to calculate the volume of the water displaced when the object was submerged.
The volume of a rectangular prism (which in this case is the volume of water displaced) is given by the formula:
Volume = length * width * height
Here, the length and width of the tank are given as 40 cm and 30 cm respectively. The height is the change in water level when the object is submerged, which is 0.25 cm.
So, the volume of the water displaced (and hence the volume of the object) is:
Volume = 40 cm * 30 cm * 0.25 cm = 300 cubic centimeters.
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