Math Problem Statement

You mass an object and determine it to be 124g. Then, you fill a graduated cylinder with water to the 53 mL mark, put the object in the graduated cylinder, and notice that the water level rises to 71 mL. What is the density of the object?

Solution

The question from the image asks you to find the density of an object based on the mass and the volume displacement in water.

Steps:

  1. Given:

    • Mass of the object = 124 g.
    • Initial water level in a graduated cylinder = 53 mL.
    • Final water level after placing the object = 71 mL.
  2. Volume of the object:

    • The volume of the object is the difference between the final and initial water levels. Volume of object=71mL53mL=18mL\text{Volume of object} = 71 \, \text{mL} - 53 \, \text{mL} = 18 \, \text{mL}
  3. Density formula: Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}} Density=124g18mL=6.89g/mL\text{Density} = \frac{124 \, \text{g}}{18 \, \text{mL}} = 6.89 \, \text{g/mL}

Answer: The density of the object is 6.89 g/mL.

Would you like a detailed explanation of these steps or further clarifications?

Here are 5 related questions for further practice:

  1. If the mass of the object were 150 g but the volume displacement remained the same, what would be the new density?
  2. How would you find the density of an irregular object without using water displacement?
  3. What would happen to the density if the object’s volume increased but its mass stayed the same?
  4. Why is the unit for density often g/mL for liquids and solids?
  5. What are the implications of an object having a density greater than 1 g/mL in water?

Tip: When calculating density using water displacement, always ensure the volume readings are accurate to avoid significant errors in the final density calculation.

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Math Problem Analysis

Mathematical Concepts

Density
Volume displacement
Mass

Formulas

Density = Mass / Volume

Theorems

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Suitable Grade Level

Grades 6-8