Question

1. a student measures the mass of an 8 cm³ block of brown sugar to be 12.9 g. what is the density of the brown sugar?
2. a chef fills a 50 ml container with 43.5 g of cooking oil. what is the density of the oil?
3. calculate the mass of a liquid with a density of 2.5 g/ml and a volume of 15 ml.
4. calculate the volume of a liquid with a density of 5.45 g/ml and a mass of 65 g.
5. a machine shop worker records the mass of an aluminum cube as 176 g. if one side of the cube measures 4 cm, what is the density of the aluminum?
6. a teacher performing a demonstration finds that a piece of cork displaces 23.5 ml of water. the piece of cork has a mass of 5.7 g. what is the density of the cork?
7. a carver begins work on the following block of granite that weighs 2700 g. what is the density of the granite?

image of a rectangular prism with length 20 cm, width 5 cm, height 10 cm

1. a piece of pvc plumbing pipe displaces 60 ml when placed into a container of water. if the pipe has a mass of 78 g, what is the density of pvc?
2. a solid magnesium flare has a mass of 1300 g and a volume of 743 cm³. what is the density of the magnesium?

Explanation:

Step1: Recall density formula

Density formula: $
ho = \frac{m}{V}$, where $
ho$ = density, $m$ = mass, $V$ = volume. For mass: $m =
ho \times V$. For volume: $V = \frac{m}{
ho}$. Note: $1\ \text{cm}^3 = 1\ \text{mL}$.

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Problem 1

Step1: Identify given values

$m = 12.9\ \text{g}$, $V = 8\ \text{cm}^3$

Step2: Calculate density

$
ho = \frac{12.9}{8} = 1.6125\ \text{g/cm}^3$

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Problem 2

Step1: Identify given values

$m = 43.5\ \text{g}$, $V = 50\ \text{mL}$

Step2: Calculate density

$
ho = \frac{43.5}{50} = 0.87\ \text{g/mL}$

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Problem 3

Step1: Identify given values

$
ho = 2.5\ \text{g/mL}$, $V = 15\ \text{mL}$

Step2: Calculate mass

$m = 2.5 \times 15 = 37.5\ \text{g}$

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Problem 4

Step1: Identify given values

$
ho = 5.45\ \text{g/mL}$, $m = 65\ \text{g}$

Step2: Calculate volume

$V = \frac{65}{5.45} \approx 11.93\ \text{mL}$

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Problem 5

Step1: Calculate cube volume

$V = 4^3 = 64\ \text{cm}^3$, $m = 176\ \text{g}$

Step2: Calculate density

$
ho = \frac{176}{64} = 2.75\ \text{g/cm}^3$

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Problem 6

Step1: Identify given values

$m = 5.7\ \text{g}$, $V = 23.5\ \text{mL}$

Step2: Calculate density

$
ho = \frac{5.7}{23.5} \approx 0.24\ \text{g/mL}$

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Problem 7

Step1: Calculate block volume

$V = 20 \times 5 \times 10 = 1000\ \text{cm}^3$, $m = 2700\ \text{g}$

Step2: Calculate density

$
ho = \frac{2700}{1000} = 2.7\ \text{g/cm}^3$

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Problem 8

Step1: Identify given values

$m = 78\ \text{g}$, $V = 60\ \text{mL}$

Step2: Calculate density

$
ho = \frac{78}{60} = 1.3\ \text{g/mL}$

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Problem 9

Step1: Identify given values

$m = 1300\ \text{g}$, $V = 743\ \text{cm}^3$

Step2: Calculate density

$
ho = \frac{1300}{743} \approx 1.75\ \text{g/cm}^3$

Answer:

1. $1.61\ \text{g/cm}^3$ (or $1.6125\ \text{g/cm}^3$)
2. $0.87\ \text{g/mL}$
3. $37.5\ \text{g}$
4. $11.93\ \text{mL}$
5. $2.75\ \text{g/cm}^3$
6. $0.24\ \text{g/mL}$
7. $2.7\ \text{g/cm}^3$
8. $1.3\ \text{g/mL}$
9. $1.75\ \text{g/cm}^3$