Math Problem Statement

Brennan's science class is learning about ways to find the volume of irregularly-shaped objects. For his first experiment, Brennan finds that a small marble statue weighs 1.3 kilograms. Then, he uses its density to find its volume in liters. If the density of marble is approximately 2.6 grams per milliliter, what is the volume of Brennan's statue? Write your answer as a whole number, decimal, or simplified fraction. Do not round.

Solution

To find the volume of Brennan's statue, we can use the formula for density:

Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}

We can rearrange this to solve for the volume:

Volume=MassDensity\text{Volume} = \frac{\text{Mass}}{\text{Density}}

Given data:

  • Mass of the statue = 1.3 kilograms
  • Density of marble = 2.6 grams per milliliter (g/mL)

Step 1: Convert the mass from kilograms to grams, because the density is given in grams per milliliter.

1 kilogram = 1000 grams, so:

1.3kg=1.3×1000=1300grams1.3 \, \text{kg} = 1.3 \times 1000 = 1300 \, \text{grams}

Step 2: Substitute the values into the formula for volume:

Volume=1300grams2.6g/mL\text{Volume} = \frac{1300 \, \text{grams}}{2.6 \, \text{g/mL}}

Volume=500mL\text{Volume} = 500 \, \text{mL}

Step 3: Convert milliliters to liters. Since 1000 milliliters = 1 liter:

500mL=5001000=0.5liters500 \, \text{mL} = \frac{500}{1000} = 0.5 \, \text{liters}

Final Answer:

The volume of Brennan's statue is 0.5 liters.

Would you like more details on this problem or have any questions?

Here are 5 related questions for further practice:

  1. What is the mass of an object if its volume is 2 liters and its density is 3.2 g/mL?
  2. How would you find the density of an object if you know its mass is 400 grams and its volume is 100 milliliters?
  3. If the volume of an object is 0.8 liters, and its density is 1.2 g/mL, what is the mass of the object?
  4. A different marble statue weighs 2.6 kg. What would be its volume in liters?
  5. How do you convert a volume from cubic centimeters (cm³) to milliliters (mL)?

Tip: When converting units, always make sure to use the appropriate conversion factor (e.g., 1 kg = 1000 g, 1 liter = 1000 mL) to maintain consistency throughout your calculations.

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Math Problem Analysis

Mathematical Concepts

Density and Volume
Unit Conversion
Ratio and Proportion

Formulas

Density = Mass / Volume
Volume = Mass / Density
1 kilogram = 1000 grams
1 liter = 1000 milliliters

Theorems

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Suitable Grade Level

Grades 6-8