Question

The initial water level in a \(10-\mathrm{mL}\) graduated cylinder reads \(4.5 \mathrm{~mL}\). After a ruby gemstone is dropped into the cylinder, the water level reads \(7.0 \mathrm{~mL}\). What is the volume of the ruby?

Short answer

The volume of the ruby is \(2.5 \mathrm{~mL}\).

Step-by-step solution

Determine the Initial Water Level

The initial water level in the graduated cylinder is given as \(4.5 \mathrm{~mL}\). This is the volume of water before any object is added.

Determine the Final Water Level

After the ruby is immersed in the cylinder, the new water level is \(7.0 \mathrm{~mL}\). This includes the volume of both the water and the ruby.

Calculate the Volume of the Ruby

To find the volume of the ruby, subtract the initial water level from the final water level: \(7.0 \mathrm{~mL} - 4.5 \mathrm{~mL} = 2.5 \mathrm{~mL}\). This difference represents the volume of the ruby.

Key concepts

Volume Measurement

Volume measurement is a fundamental concept in experiments involving liquids and solids. It refers to determining how much space an object or substance occupies.
To measure the volume of a liquid, tools like graduated cylinders, pipettes, or beakers are commonly used. These tools have measurement markings, typically in milliliters or liters, to help determine the liquid volume accurately.
In our example, a graduated cylinder is used because it allows for precise measurement of both liquid and small solid objects through visible scale readings.
When measuring, it is important to observe the bottom of the meniscus, which is the curved surface of the liquid. This ensures that the reading is accurate. Even slight misjudgments can alter the results, underlining the importance of careful observation.

Water Displacement Method

The water displacement method is a clever technique for measuring the volume of irregularly shaped objects, such as gemstones. This method capitalizes on Archimedes' principle, which states that the volume of the displaced water equals the volume of the immersed object.
To apply the water displacement method, first measure the initial water level in a graduated cylinder. Then, submerge the object completely in the water and record the new water level. The change in water level, or water displacement, gives the volume of the object.
For example, in the exercise with the ruby gemstone, the initial water level was 4.5 mL, and after immersing the gemstone, the water level rose to 7.0 mL. By subtracting the initial level from the new level—7.0 mL minus 4.5 mL—we can determine that the ruby has a volume of 2.5 mL.

Liquid Volume

Liquid volume refers to the amount of space that a liquid occupies, usually measured in milliliters (mL) or liters (L). In scientific experiments, accurately determining liquid volume is crucial for precise results and analysis.
To accurately measure liquid volume, it's important to use clean and calibrated measurement devices, like graduated cylinders. The accuracy of these instruments ensures reliable experimental data.
Liquids have no fixed shape and will take the shape of their container, making precise measurement markings and a flat observation surface essential for accuracy. In our scenario with the graduated cylinder, the initial and final liquid volumes are used to deduce the volume of an object submerged in the liquid, demonstrating practical application of liquid volume measurement in a physical setting.