Question

ws 1.5 density problems (be certain to specify final units)

1. you have a rock with a volume of 15 cm³ and a mass of 45 g. what is its density? (3.0)
2. you have a different rock with a volume of 30 cm³ and a mass of 60 g. what is its density? (2)
3. in the above two examples which rock is heavier? which is lighter?
4. you decide you want to carry a boulder home from the beach. it is 30.0 centimeters on each side. it is made of granite, which has a typical density of 2.80 g/cm³. what is the boulder’s mass? (7.56×10⁴)
5. rocks are sometimes used along coasts to prevent erosion. if a rock needs to weigh 2.010 kilograms (about 2 tons) in order not to be shifted by waves, what volume does it need to be? you are using basalt, which has a typical density of 3210 kg/m³. (0.626)
6. a golden-colored cube is handed to you. the person wants you to buy it for $100, saying that is a gold nugget. you pull out your old geology text and look up gold in the mineral table, and read that its density is 19.3 g/cm³. you measure the cube and find that it is 2.0 cm on each side, and has a mass of 40.0 g. what is its density? is it gold? should you buy it? (5.0)
7. the density of paper is 1.20 g/cm³. what is the mass of the paper in a notebook that is 76 mm thick, 215.9 mm wide, and 279.4 mm long? express your answer in significant digits. (5.5×10²)
8. in pottery class, you throw a pot from a lump of wet clay. your pot’s mass is 5.5 kg. after the pot is fired, its mass is 4.9 kg. the density of wet clay is 1.60 g/cm³ and the density of fired clay is 1.36 g/cm³. what was the volume of your pot before it was fired? what was the volume of the pot after it was fired? express your answer in significant digits. (3400; 3600)
9. the italian government is giving michelangelo’s david a bath. in the newspaper, there was a photo of a person working on the statue. their hand was half the size of the statue’s hand. if the statue is 4.9 m³ and the density of marble is 2.76 g/cm³ what is the mass? express your answer in significant digits. (1.4×10⁷)
10. the volume of the aquarium in a classroom is 1890 l. the density of seawater is 1.03 g/ml. what is the mass of the water in the tank? express your answer in significant digits. (1,950,000)

Explanation:

Step1: Density formula

$
ho = \frac{m}{V}$

Step2: Substitute values

$
ho = \frac{45\ \text{g}}{15\ \text{cm}^3} = 3.0\ \text{g/cm}^3$

Step1: Density formula

$
ho = \frac{m}{V}$

Step2: Substitute values

$
ho = \frac{60\ \text{g}}{30\ \text{cm}^3} = 2\ \text{g/cm}^3$

Step1: Compare masses

First rock: 45 g; Second rock: 60 g

Step1: Volume of cube

$V = a^3 = (30.0\ \text{cm})^3 = 27000\ \text{cm}^3$

Step2: Mass formula

$m =
ho V = 2.80\ \text{g/cm}^3 \times 27000\ \text{cm}^3 = 7.56 \times 10^4\ \text{g}$

Answer:

3.0 g/cm³