# 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 |

- ACobalt
- BAluminum
- CCopper

**Q3: **

A small cube of iron has sides with length 0.15 m. If the mass of the cube is 26.6 kg, what is its density? Give your answer to 3 significant figures.

**Q4: **

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

**Q5: **

Gold can be hammered into very thin sheets. If a thin sheet of gold is 30 cm wide and 40 cm
long and has a mass of 9.4 g, find the thickness of the sheet. Use a value of 19 320 kg/m^{3} for the density of gold. Give your answer in millimeters to 2 significant figures.

**Q6: **

It is worked out that a solid gold crown has a volume of 150 cm^{3}. Find the mass of the gold crown, using a value of 19 300 kg/m^{3} for the density of gold. Give your answer to 2 significant figures.

**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 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 cuboid 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?

**Q13: **

The masses and volumes of 5 objects are measured and the results are plotted on the shown graph. Which object has the highest density?

- AObject
- BObject
- CObject
- DObject
- EObject

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

Which sphere has the lowest density?

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

**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 kg/m^{3} for the density of steel.

**Q16: **

Henry 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. Daniel 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 kg/m^{3}. What value does he get for the volume of polystyrene used in cubic centimeters? Give your answer to 3 significant figures.