# Worksheet: Calculating Density

In this worksheet, we will practice using the formula ρ = M/V to calculate the densities of different materials and objects.

**Q2: **

A scientist has three cubes of different materials. Each cube has a volume of
125 cm^{3}. She weighs each cube to find its mass,
and her results are recorded in the table shown. Which material has the highest density?

Material | Volume (cm^{3}) | Mass (kg) |
---|---|---|

Aluminum | 125 | 0.339 kg |

Copper | 125 | 1.12 kg |

Cobalt | 125 | 1.09 kg |

- AAluminum
- BCopper
- CCobalt

**Q4: **

A cube has a mass of 30 kg. If the
volume of the cube is 0.02 m^{3}, what is
its density?

**Q7: **

A barrel of crude oil has a volume of 0.159 m^{3}. Find the mass of the oil contained by the barrel, using a value of 900 kg/m^{3} for the density of oil.

**Q8: **

Find the volume of a 54 kg block of aluminum. Use a value of 2,700 kg/m^{3} for the density of aluminum.

**Q9: **

A bowling ball has a mass of 5.5 kg. The bowling ball is a sphere with a radius of 7 cm. What is the density of the bowling ball? Give your answer to 2 significant figures.

**Q10: **

A brick has a mass of 3.5 kg. It is a rectangular prism with side lengths of 23 cm, 11 cm, and 7 cm. What is the density of the brick? Give your answer to 3 significant figures.

**Q11: **

A zinc cube is lowered into a cylinder of water to work out its volume. The cylinder has a diameter of 5 cm, and when the cube is lowered into it, the level of the water rises by 12 mm.

What is the radius of the cylinder?

Which of the following is the correct formula for the volume of a cylinder?

- A
- B
- C
- D

What is the volume of the cube? Give your answer to 3 significant figures.

What is the length of one side of the cube? Give your answer to 3 significant figures.

The mass of the zinc cube is 168 g. What is the density of zinc? Give your answer to 4 significant figures.

**Q12: **

Two spheres have the same density, but the first sphere has a volume 10 times greater than that of the second. How much greater is the mass of the first sphere than that of the second sphere?

**Q14: **

Mason has four spheres. Each is made out of a different material and each has a different mass and volume. Mason wants to know which sphere has the highest density. He measures the diameter and mass of each sphere. His results are recorded in the table shown.

Sphere | Diameter (cm) | Mass (kg) |
---|---|---|

A | 10.0 | 8.40 kg |

B | 12.0 | 14.2 kg |

C | 6.00 | 9.10 kg |

D | 15.00 | 20.3 kg |

What is the volume of sphere A? Give your answer to 3 significant figures.

- A m
^{3} - B m
^{3} - C m
^{3} - D m
^{3}

What is the density of sphere A? Give your answer to 2 significant figures.

Which sphere has the highest density?

- ASphere B
- BSphere A
- CSphere D
- DSphere C

Which sphere has the lowest density?

- ASphere A
- BSphere B
- CSphere D
- DSphere C

**Q15: **

A steel ball bearing has a mass of 0.034 g. Find the diameter of the ball bearing in millimeters, rounded to the nearest millimeter. Use a value of 8,000 kg/m^{3} for the density of steel.

**Q16: **

Michael orders an item from an online shop. It is delivered in a cardboard box.
To protect the item, hundreds of small pieces of polystyrene surround it in the box.
Michael wants to know what volume of polystyrene was used. He weighs the polystyrene
and finds it has a mass of 450 g. He knows that polystyrene has a density
of 1,040 kg/m^{3}. What value does he get for the volume of polystyrene used in
cubic centimeters? Give your answer to 3 significant figures.

**Q17: **

Which of the following is the correct formula for finding the density , of an object given its mass , and its volume ?

- A
- B
- C
- D
- E

**Q18: **

The density of iron is 7.874 g/cm^{3}.
What is this value in kilograms per cubic meter?

**Q19: **

Two equal volumes of different materials are mixed together. If their densities are
2βββ500 kg/m^{3} and 5βββ500 kg/m^{3},
then the average density of the mixture equals .

- A4βββ250 kg/m
^{3} - B4βββ000 kg/m
^{3} - C3βββ500 kg/m
^{3} - D3βββ000 kg/m
^{3}

**Q20: **

The table shows the density of some materials at the same temperature. If we have one kilogram of each material, which of them will have the smallest volume?

Material | Iron | Silver | Tungsten | Aluminium |
---|---|---|---|---|

Density (kg/m^{3}) | 7,860 | 10,497 | 19,450 | 2,705 |

- ASilver
- BAluminium
- CTungsten
- DIron

**Q21: **

A cuboid made of iron has a width of
12 cm, a length of
10 cm, a mass of
0.5 kg,
and a density of
7.9 g/cm^{3}.
What is its height?

- A3 cm
- B7 cm
- C2 cm
- D10 cm

**Q22: **

The given figure shows two cylinders of different materials that have the same radius. If the mass of the first cylinder is double that of the second cylinder and the height of the first cylinder is half that of the second cylinder, then the ratio between their densities is .

- A2
- B
- C4
- D

**Q23: **

The figure shows a cylinder of uniform cross-sectional area, closed from both sides and containing a frictionless piston trapping two different amounts of air at its sides such that the pressure on its sides is 100 cmHg. If the piston is moved slowly to the middle of the cylinder, then the pressure difference between the two sides of the piston becomes .

- A160 cmHg
- B100 cmHg
- C120 cmHg
- D40 cmHg

**Q24: **

A rectangular prism made of substance A that has a mass of 10.25 kg and dimensions of 15 cm, 25 cm, and 3 cm is compared to another rectangular prism made of substance B that has a mass of 5.62 kg and dimensions of 12 cm, 25 cm, and 5 cm. Calculate the ratio between the density of substance B and that of substance A.

- A2.43
- B0.41
- C0.73
- D1.37

**Q25: **

Which of the following graphs represents the relation between the density of a block of iron () and its volume ()?

- A
- B
- C
- D