Question

introduction to matter : ... measuring matter
understanding main ideas
use the figure below to answer the following questions. write and discuss in a ...

1. what is the volume of the solid in the figure? show your work. be sure to use correct units of measurement.

image of a rectangular solid with 3 cm, 3 cm, 10 cm

1. the solid has a mass of 180 g. what is the density of the solid? show your work. be sure to use correct units of measurement.
2. would the above solid have a mass of 180 g on the moon? would it have the same weight on earth as on the moon? explain your answers.
3. the solid above sinks to the bottom when you put it in a container filled with water. what does that tell you about its density?
4. will every solid with the same dimensions have the same density? explain your answer.

building vocabulary
write a definition for each of the following terms on the lines below.

1. mass
2. volume
3. density
4. give two examples of common units for each of the above measurements.

Explanation:

Answer:

1. The solid is a rectangular prism (or cuboid). The formula for the volume \( V \) of a rectangular prism is \( V = l \times w \times h \). From the figure, the length \( l = 10 \, \text{cm} \), width \( w = 3 \, \text{cm} \), and height \( h = 3 \, \text{cm} \). So, \( V = 10 \times 3 \times 3 = 90 \, \text{cm}^3 \).
2. Density \(

ho \) is given by the formula \(
ho = \frac{m}{V} \), where \( m \) is mass and \( V \) is volume. Here, \( m = 180 \, \text{g} \) and \( V = 90 \, \text{cm}^3 \). So, \(
ho = \frac{180}{90} = 2 \, \text{g/cm}^3 \).

1. Mass is an intrinsic property (amount of matter) and does not change with location, so the mass on the moon would still be \( 180 \, \text{g} \). Weight depends on gravity (\( W = mg \)), and the moon’s gravity is less than Earth’s, so the weight would be different (less on the moon).
2. If an object sinks in water, its density is greater than the density of water (water’s density is \( 1 \, \text{g/cm}^3 \), and the solid’s density is \( 2 \, \text{g/cm}^3 \), which is greater).
3. No. Density depends on mass (and volume), and solids with the same dimensions (same volume) can have different masses (e.g., different materials like iron vs. wood in the same - sized block), so their densities would differ.
4. Mass: A measure of the amount of matter in an object.
5. Volume: The amount of space that a substance or object occupies (or the capacity of a container to hold a substance).
6. Density: The mass of a substance per unit volume (mathematically, \(

ho=\frac{m}{V} \), where \(
ho \) is density, \( m \) is mass, and \( V \) is volume).

1. - Mass: grams (g), kilograms (kg)

• Volume: cubic centimeters (\( \text{cm}^3 \)), liters (L)
• Density: grams per cubic centimeter (\( \text{g/cm}^3 \)), kilograms per cubic meter (\( \text{kg/m}^3 \))