density calculations
density
m
d v
d = $\frac{m}{v}$
divide
mass
m
d v
m = d*v
multiply
volume
m
d v
v = $\frac{m}{d}$
divide
1. a student measures the mass of an 8 cm3 block of brown sugar to be 12.9 g. what is the density of brown sugar? 1.6
2. a chef fills a 50 ml container with 43.5 g of cooking oil. what is the density of the oil? 0.87
3. calculate the mass of a liquid with a density of 2.5 g/ml and a volume of 15 ml. 37.5
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 granite?
(image of a rectangular prism with length 20 cm, width 5 cm, height 10 cm)

Question

Accepted Answer

### Problem 1:
# Explanation:
## Step1: Identify formula for density
Density formula is $ D = \frac{M}{V} $, where $ M = 12.9 \, \text{g} $, $ V = 8 \, \text{cm}^3 $.
## Step2: Substitute values into formula
$ D = \frac{12.9}{8} $
## Step3: Calculate the result
$ D = 1.6125 \, \text{g/cm}^3 \approx 1.6 \, \text{g/cm}^3 $
# Answer: $ 1.6 \, \text{g/cm}^3 $

### Problem 2:
# Explanation:
## Step1: Identify formula for density
$ D = \frac{M}{V} $, $ M = 43.5 \, \text{g} $, $ V = 50 \, \text{mL} $.
## Step2: Substitute values
$ D = \frac{43.5}{50} $
## Step3: Compute
$ D = 0.87 \, \text{g/mL} $
# Answer: $ 0.87 \, \text{g/mL} $

### Problem 3:
# Explanation:
## Step1: Identify formula for mass
$ M = D \times V $, $ D = 2.5 \, \text{g/mL} $, $ V = 15 \, \text{mL} $.
## Step2: Substitute values
$ M = 2.5 \times 15 $
## Step3: Calculate
$ M = 37.5 \, \text{g} $
# Answer: $ 37.5 \, \text{g} $

### Problem 4:
# Explanation:
## Step1: Identify formula for volume
$ V = \frac{M}{D} $, $ M = 65 \, \text{g} $, $ D = 5.45 \, \text{g/mL} $.
## Step2: Substitute values
$ V = \frac{65}{5.45} $
## Step3: Compute (approximate)
$ V \approx 11.93 \, \text{mL} $ (if needed to round, depends on context, but exact is $ \frac{65}{5.45} \approx 11.93 $)
# Answer: $ \approx 11.93 \, \text{mL} $ (or exact $ \frac{1300}{109} \approx 11.93 $)

### Problem 5:
# Explanation:
## Step1: Find volume of cube
Volume of cube $ V = s^3 $, $ s = 4 \, \text{cm} $, so $ V = 4^3 = 64 \, \text{cm}^3 $.
## Step2: Identify density formula
$ D = \frac{M}{V} $, $ M = 176 \, \text{g} $, $ V = 64 \, \text{cm}^3 $.
## Step3: Substitute and calculate
$ D = \frac{176}{64} = 2.75 \, \text{g/cm}^3 $
# Answer: $ 2.75 \, \text{g/cm}^3 $

### Problem 6:
# Explanation:
## Step1: Volume of cork (water displacement)
Volume $ V = 23.5 \, \text{mL} = 23.5 \, \text{cm}^3 $ (since $ 1 \, \text{mL} = 1 \, \text{cm}^3 $).
## Step2: Density formula
$ D = \frac{M}{V} $, $ M = 5.7 \, \text{g} $, $ V = 23.5 \, \text{cm}^3 $.
## Step3: Calculate
$ D = \frac{5.7}{23.5} \approx 0.2425 \, \text{g/cm}^3 \approx 0.24 \, \text{g/cm}^3 $ (or more precise $ \approx 0.24 $)
# Answer: $ \approx 0.24 \, \text{g/cm}^3 $ (exact $ \frac{57}{235} \approx 0.2425 $)

### Problem 7:
# Explanation:
## Step1: Find volume of rectangular block
Volume $ V = l \times w \times h $, $ l = 20 \, \text{cm} $, $ w = 5 \, \text{cm} $, $ h = 10 \, \text{cm} $, so $ V = 20 \times 5 \times 10 = 1000 \, \text{cm}^3 $.
## Step2: Density formula
$ D = \frac{M}{V} $, $ M = 2700 \, \text{g} $, $ V = 1000 \, \text{cm}^3 $.
## Step3: Calculate
$ D = \frac{2700}{1000} = 2.7 \, \text{g/cm}^3 $
# Answer: $ 2.7 \, \text{g/cm}^3 $

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QUESTION IMAGE

Question

Explanation:

Problem 1:

Step1: Identify formula for density

Step2: Substitute values into formula

Step3: Calculate the result

Step1: Identify formula for density

Step2: Substitute values

Step3: Compute

Step1: Identify formula for mass

Step2: Substitute values

Step3: Calculate

Answer:

Problem 2: