A graduated cylinder is filled to 10.1 cm3 with water and a piece of silicon dioxide is placed in the cylinder, displacing the level to 24.6 cm3. What is the volume of the silicon dioxide piece in cubic centimeters?
Answer (2)
The problem gives the initial and final water levels in a graduated cylinder after adding silicon dioxide.
The volume of the silicon dioxide is the difference between the final and initial volumes.
Calculate the difference: 24.6 c m 3 − 10.1 c m 3 = 14.5 c m 3 .
The volume of the silicon dioxide piece is 14.5 c m 3 .
Explanation
Problem Analysis We are given that a graduated cylinder is initially filled with water to a volume of 10.1 c m 3 . When a piece of silicon dioxide is added, the water level rises to 24.6 c m 3 . Our goal is to find the volume of the silicon dioxide.
Finding the Volume The volume of the silicon dioxide is equal to the difference between the final water level and the initial water level. So, we subtract the initial volume from the final volume to find the volume of the silicon dioxide piece.
Calculations Let V ini t ia l be the initial volume of water, and V f ina l be the final volume after adding the silicon dioxide. Then the volume of the silicon dioxide, V s i l i co n _ d i o x i d e , is given by:
V s i l i co n _ d i o x i d e = V f ina l − V ini t ia l
Substituting the given values:
V s i l i co n _ d i o x i d e = 24.6 c m 3 − 10.1 c m 3
V s i l i co n _ d i o x i d e = 14.5 c m 3
Final Answer Therefore, the volume of the silicon dioxide piece is 14.5 c m 3 .
Examples
This concept is useful in various real-world scenarios, such as determining the volume of irregularly shaped objects. For instance, if you want to find the volume of a small rock, you can use a graduated cylinder filled with water. By measuring the water level before and after submerging the rock, you can calculate the rock's volume. This method is commonly used in science and engineering for accurate volume measurements.
The volume of the silicon dioxide piece added to the graduated cylinder is 14.5 cm³, calculated by subtracting the initial water level from the final water level after the silicon dioxide was added. This calculation uses the formula for volume displacement. Therefore, the volume is 14.5 c m 3 .
;
