Q: A cube of platinum has a side length of 0.75 cm. If the density of platinum is 21.4 g/cm$$^3$$, what is the mass of the cube in grams?

$$0.75 \times 0.75 \times 0.75 \times 21.4 = 9.04 g$$

Q: A copper wire (density = 8.96 g/cm$$^3) $$has a diameter of 0.32 mm. If a sample of this copper wire has a mass of 21.7 g, what is the length of the wire in cm? (Use $$V = \pi r^2$ h$$ for a cylinder.)

$$\frac{21.7}{8.96 \times \pi \times (0.016)^2$} = 30.0 cm$$

Q: If the density of a certain spherical atomic nucleus is $$1.0 \times 10$$^{14}$$ g/cm^3$ and its mass is 3.5$$ \times $$10^{-23} g$$, what is the radius in angstroms? ($$V = \frac{4}{3}\pi r^3$; 1$ cm $$= $$10^8$$ Å)

$$r = \left( \frac{3.5 \times 10$$^{-23}$$}{1.0 \times 10$$^{14}$$ \times \frac{4}{3}\pi} \$$right)^{1/3}$$ \times 10^8$ = 10,376,800.5$$ Å

Q: A silver cube has a side length of 0.56 cm and a density of 10.5 g/cm$$^3. $$What is its mass in kilograms?

$$0.56^3$$ \times 10.5 \div 1000 = 0.018$$ kg

Q: A student measures the mass and volume of a sample and calculates its density. Which equation should they use?

$$\text{Density} = \frac{\text{Mass}}{\text{Volume}}$$

Q: A rectangular block has dimensions 2.0 cm × 3.0 cm × 4.0 cm. What is its volume?

$$V = 2.0 \times 3.0 \times 4.0 = 24.0 cm$^3$$

Q: A cylindrical rod has a radius of 0.5 cm and a height of 10.0 cm. What is its volume?

$$V = \pi (0.5)^2$ \times 10.0 = 7.85 cm$^3$$

Question 1

A cube of platinum has a side length of 0.75 cm. If the density of platinum is 21.4 g/cm$$^3$$, what is the mass of the cube in grams?

Accepted Answer

$$0.75 	imes 0.75 	imes 0.75 	imes 21.4 = 9.04 g$$

Question 2

A copper wire (density = 8.96 g/cm$$^3) $$has a diameter of 0.32 mm. If a sample of this copper wire has a mass of 21.7 g, what is the length of the wire in cm? (Use $$V = \pi r^2$ h$$ for a cylinder.)

Accepted Answer

$$\frac{21.7}{8.96 	imes \pi 	imes (0.016)^2$} = 30.0 cm$$

Question 3

If the density of a certain spherical atomic nucleus is $$1.0 	imes 10$$^{14}$$ g/cm^3$ and its mass is 3.5$$ 	imes $$10^{-23} g$$, what is the radius in angstroms? ($$V = \frac{4}{3}\pi r^3$; 1$ cm $$= $$10^8$$ Å)

Accepted Answer

$$r = \left( \frac{3.5 	imes 10$$^{-23}$$}{1.0 	imes 10$$^{14}$$ 	imes \frac{4}{3}\pi} \$$right)^{1/3}$$ 	imes 10^8$ = 10,376,800.5$$ Å

Question 4

A silver cube has a side length of 0.56 cm and a density of 10.5 g/cm$$^3. $$What is its mass in kilograms?

Accepted Answer

$$0.56^3$$ 	imes 10.5 \div 1000 = 0.018$$ kg

Question 5

Which formula would you use to calculate the volume of a cylinder?

Accepted Answer

$$V = \pi r^2$ h$$

Question 6

A student measures the mass and volume of a sample and calculates its density. Which equation should they use?

Accepted Answer

$$	ext{Density} = \frac{	ext{Mass}}{	ext{Volume}}$$

Question 7

A spherical object has a radius of 2.0 cm. What is its volume?

Accepted Answer

$$V = \frac{4}{3}\pi (2.0)^3$ = 33.51 cm$^3$$

Question 8

A rectangular block has dimensions 2.0 cm × 3.0 cm × 4.0 cm. What is its volume?

Accepted Answer

$$V = 2.0 	imes 3.0 	imes 4.0 = 24.0 cm$^3$$

Question 9

A sample of metal has a mass of 50.0 g and a volume of 10.0 cm$$^3. $$What is its density?

Accepted Answer

$$\frac{50.0}{10.0} = 5.0 g/cm$^3$$

Question 10

A cylindrical rod has a radius of 0.5 cm and a height of 10.0 cm. What is its volume?

Accepted Answer

$$V = \pi (0.5)^2$ 	imes 10.0 = 7.85 cm$^3$$

Question 11

A cube of gold has a mass of 19.3 g and a side length of 1.0 cm. What is the density of gold?

Accepted Answer

$$\frac{19.3}{1.0^3$} = 19.3 g/cm$^3$$

Question 12

A student is given a sample of unknown metal. The sample has a mass of 8.96 g and a volume of 1.0 cm$$^3. $$Which metal is it most likely to be, based on density?

Accepted Answer

Copper (density = 8.96 g/cm$$^3)$$

Question 13

A sphere has a mass of 33.5 g and a radius of 2.0 cm. What is its density?

Accepted Answer

$$\frac{33.5}{\frac{4}{3}\pi (2.0)^3$} = 1.0 g/cm$^3$$

Question 14

A cube of unknown material has a mass of 5.0 g and a side length of 1.0 cm. If the density of the material is less than water, what will happen if the cube is placed in water?

Accepted Answer

It will float.

Question 15

A cylinder has a radius of 1.0 cm and a height of 5.0 cm. If its mass is 15.7 g, what is its density?

Accepted Answer

$$\frac{15.7}{\pi (1.0)^2$ 	imes 5.0} = 1.0 g/cm$^3$$

Question 16

A cube of lead has a side length of 2.0 cm and a density of 11.3 g/cm$$^3. $$What is its mass?

Accepted Answer

$$2.0^3$$ 	imes 11.3 = 90.4$$ g

Question 17

A sphere has a volume of 33.5 cm$$^3$$ and a mass of 67.0 g. What is its density?

Accepted Answer

$$\frac{67.0}{33.5} = 2.0 g/cm$^3$$

Question 18

A student is given a cylinder with a radius of 0.5 cm and a height of 10.0 cm. If the density of the material is 2.0 g/cm$$^3$$, what is the mass of the cylinder?

Accepted Answer

$$\pi (0.5)^2$ 	imes 10.0 	imes 2.0 = 15.7 g$$

Density, Volume, and Mass Calculations for Geometric Objects

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