Density：練習問題

Which equation correctly defines the density \(\rho\) of a substance of mass \(m\) and volume \(V\)?

A student determines the density of an irregularly shaped metal object. The object has a mass of \(156 \text{ g}\). When placed in a measuring cylinder containing \(50 \text{ cm}^3\) of water, the water level rises to \(80 \text{ cm}^3\).
What is the density of the metal?

A hollow cylindrical metal pipe has an outer radius of \(3.0\text{ cm}\), an inner radius of \(2.0\text{ cm}\), and a length of \(20.0\text{ cm}\).
The density of the metal is \(7.0\text{ g/cm}^3\).
What is the mass of the pipe? (Take \(\pi = 3.14\))

The table shows the masses and volumes of four solid objects.
Which object has the greatest density?

Object P: mass \(= 40\text{ g}\), volume \(= 20\text{ cm}^3\)
Object Q: mass \(= 60\text{ g}\), volume \(= 15\text{ cm}^3\)
Object R: mass \(= 90\text{ g}\), volume \(= 45\text{ cm}^3\)
Object S: mass \(= 100\text{ g}\), volume \(= 50\text{ cm}^3\)

A rectangular wooden block has dimensions \(5.0\text{ cm} \times 4.0\text{ cm} \times 10.0\text{ cm}\). The block has a mass of \(160\text{ g}\).
What is the density of the wood in \(\text{kg/m}^3\)?

A small piece of plastic has a mass of \(18\text{ g}\) and a volume of \(20\text{ cm}^3\). Calculate its density and state whether it will float or sink when placed in pure water of density \(1.0\text{ g/cm}^3\).

A glass bottle has a mass of \(50.0\text{ g}\) when empty. When completely filled with water (density \(1.00\text{ g/cm}^3\)), the total mass is \(150.0\text{ g}\). When filled with an unknown oil, the total mass is \(132.0\text{ g}\). Calculate the density of the oil.

A hollow brass cylinder has an outer radius of \(3.0\text{ cm}\), an inner radius of \(2.0\text{ cm}\), and a length of \(10.0\text{ cm}\). The density of brass is \(8.5\text{ g/cm}^3\). Calculate the mass of the hollow cylinder. (Take \(\pi \approx 3.14\))

A solid rectangular block of plastic has the dimensions shown in the diagram.

(a) Calculate the volume of the block in \(\text{cm}^3\).
(b) The mass of the block is measured using a balance and found to be \(192\text{ g}\). Calculate the density of the plastic in \(\text{g/cm}^3\).
(c) State, with a reason, whether this plastic block will float or sink when placed in pure water (density of water = \(1.0\text{ g/cm}^3\)).

A metal cube has sides of length \(0.040\text{ m}\). The density of the metal is \(7800\text{ kg/m}^3\).

(a) Calculate the volume of the cube in \(\text{m}^3\).
(b) Calculate the mass of the cube in \(\text{kg}\).
(c) The gravitational field strength is \(g = 9.8\text{ N/kg}\). Calculate the weight of the cube.
(d) A cylindrical hole of cross-sectional area \(2.0 \times 10^{-4}\text{ m}^2\) is drilled completely through from the top face to the bottom face of the cube. Calculate the new mass of the cube.