Question

density word problems
answer the word problems using the formulas listed below. you must show your work.
d = m/v and v = lxwxh, v = vf - vi mass = g volume = cm³ or ml

1. 216 g of salt has a volume of 100 cm3. what is the density?
2. a ball has a mass of 46.9 g and a volume of 40.5 cm3. what is the density?
3. a gold coin has a mass of 38.4 g and a volume of 2 cm3. what is the density?
4. a bowl of pennies has a mass of 650 g and a volume of 100 cm3. what is the density?
5. a candle has a mass of 3.72 g and volume of 4 cm3. what is the density?
6. a glass ornament has a mass of 10.55 g and a volume of 5 cm3. what is the density?
7. a block of wood has a length of 10.2 cm, width of 6 cm, and height of 4.1 cm. the wood has a total mass of 179 g. what is the volume and the density of the wood?

Explanation:

Step1: Recall the density formula

The formula for density is \(D = \frac{M}{V}\), where \(D\) is density, \(M\) is mass, and \(V\) is volume.

Step2: Substitute the values for each problem

Problem 1

Given \(M = 210\space g\) and \(V=100\space cm^{3}\).
Substitute into the formula: \(D=\frac{210}{100}\)
\(D = 2.1\space g/cm^{3}\)

Problem 2

Given \(M = 46.9\space g\) and \(V = 40.5\space cm^{3}\)
\(D=\frac{46.9}{40.5}\approx1.16\space g/cm^{3}\)

Problem 3

Given \(M = 38.4\space g\) and \(V = 2\space cm^{3}\)
\(D=\frac{38.4}{2}=19.2\space g/cm^{3}\)

Problem 4

Given \(M = 650\space g\) and \(V = 100\space cm^{3}\)
\(D=\frac{650}{100}=6.5\space g/cm^{3}\)

Problem 5

Given \(M = 3.72\space g\) and \(V = 4\space cm^{3}\)
\(D=\frac{3.72}{4}=0.93\space g/cm^{3}\)

Problem 6

Given \(M = 10.55\space g\) and \(V = 5\space cm^{3}\)
\(D=\frac{10.55}{5}=2.11\space g/cm^{3}\)

Problem 7

First, find the volume using \(V = L\times W\times H\)
Given \(L = 10.2\space cm\), \(W = 6\space cm\), \(H = 4.1\space cm\)
\(V=10.2\times6\times4.1\)
\(V = 10.2\times24.6=250.92\space cm^{3}\)
Then find the density. Given \(M = 179\space g\)
\(D=\frac{179}{250.92}\approx0.71\space g/cm^{3}\)

Answer:

1. \(2.1\space g/cm^{3}\)
2. \(\approx1.16\space g/cm^{3}\)
3. \(19.2\space g/cm^{3}\)
4. \(6.5\space g/cm^{3}\)
5. \(0.93\space g/cm^{3}\)
6. \(2.11\space g/cm^{3}\)
7. Volume: \(250.92\space cm^{3}\), Density: \(\approx0.71\space g/cm^{3}\)