Math Problem Statement

Use the image to determine the volume of the rock.

Solution

To calculate the volume of the irregular solid (rock) using the image, we need to follow these steps:

  1. Initial Volume (Before Rock is Submerged):

    • From the left beaker, the liquid level is at 20 mL.
  2. Final Volume (After Rock is Submerged):

    • From the right beaker, the liquid level is at 30 mL.
  3. Volume of the Rock:

    • The volume of the rock is determined by the difference between the final volume and the initial volume: Volume of rock=Final volumeInitial volume\text{Volume of rock} = \text{Final volume} - \text{Initial volume} Volume of rock=30mL20mL=10mL\text{Volume of rock} = 30 \, \text{mL} - 20 \, \text{mL} = 10 \, \text{mL}

Since 1mL=1cm31 \, \text{mL} = 1 \, \text{cm}^3, the volume of the rock is:

Volume of rock=10cm3\text{Volume of rock} = 10 \, \text{cm}^3

Would you like more details or have any questions?

Here are five related questions:

  1. What is Archimedes' principle, and how does it relate to this method?
  2. How can this method be applied to calculate the volume of other irregular objects?
  3. What other units can be used to measure volume besides mL and cm³?
  4. Why does the water level rise when the rock is submerged?
  5. What factors could affect the accuracy of this volume measurement?

Tip: Always make sure the object being measured is fully submerged to get an accurate volume using water displacement.

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Math Problem Analysis

Mathematical Concepts

Measurement
Volume Calculation
Water Displacement Method

Formulas

Volume of rock = Final volume - Initial volume

Theorems

Archimedes' Principle

Suitable Grade Level

Grades 6-8