Question
30. In the figure to the right, I placed an irregular shaped object in a graduated cylinder that contained 60 mL of water in it. After the irregular shaped object sunk to the bottom, read the bottom of the meniscus, and the water rose to 90 mL . What is the volume of the irregular shaped object?
Ask by Little Colon. in the United States
Jan 21,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The volume of the irregularly shaped object is 30 mL.
Solution
To determine the volume of the irregularly shaped object using the water displacement method, follow these steps:
1. **Initial Volume of Water:**
The graduated cylinder initially contains **60 mL** of water.
2. **Volume After Object is Placed:**
After placing the object in the cylinder, the water level rises to **90 mL**.
3. **Calculate the Displaced Water:**
The difference in water volume before and after adding the object represents the volume of the object.
\[
\text{Volume of Object} = \text{Final Volume} - \text{Initial Volume} = 90\, \text{mL} - 60\, \text{mL} = 30\, \text{mL}
\]
**Answer:**
The volume of the irregularly shaped object is **30 mL**.
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Simplify this solution Beyond the Answer
The volume of the irregular shaped object can be determined by using the water displacement method. Since the water level rose from 60 mL to 90 mL after the object was submerged, you simply subtract the original water level from the new water level: 90 mL - 60 mL = 30 mL. Therefore, the volume of the irregular shaped object is 30 mL. This method of measuring volume through displacement is based on Archimedes' principle, which dates back to ancient Greece. Archimedes discovered that when an object is submerged in a fluid, it displaces an amount of fluid equal to its own volume. This principle laid the groundwork for fluid mechanics and remains a fundamental concept in physics today!
