Math

QuestionFind the density of a metal cube (1.50 cm sides) weighing 4.32 g in g/ml\mathrm{g} / \mathrm{ml}. Report with sig. figs.

Studdy Solution

STEP 1

Assumptions1. The metal sample is cut into a cube. Each side of the cube is1.50 cm in length3. The weight of the sample is4.32 g4. The density of the metal is to be found in g/ml5. The density is defined as mass/volume

STEP 2

First, we need to find the volume of the cube. The volume of a cube is given by the cube of the length of its side.
Volume = Side\, length^

STEP 3

Now, plug in the given value for the side length to calculate the volume.
Volume=(1.50cm)3Volume = (1.50\, cm)^3

STEP 4

Calculate the volume of the cube.
Volume=(1.50cm)3=3.375cm3Volume = (1.50\, cm)^3 =3.375\, cm^3

STEP 5

Now, we need to convert the volume from cm3cm^3 to mlml because the density is asked in g/mlg/ml. We know that 1cm3=1ml1 cm^3 =1 ml.
Volume=3.375cm3=3.375mlVolume =3.375\, cm^3 =3.375\, ml

STEP 6

Now that we have the volume, we can find the density of the metal. Density is defined as mass/volume.
Density=Mass/VolumeDensity = Mass / Volume

STEP 7

Plug in the values for the mass and the volume to calculate the density.
Density=4.32g/3.375mlDensity =4.32\, g /3.375\, ml

STEP 8

Calculate the density of the metal.
Density=4.32g/3.375ml=1.28g/mlDensity =4.32\, g /3.375\, ml =1.28\, g/mlThe density of the metal is 1.28g/ml1.28\, g/ml.

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