Two spheres are measured and are both found to have a mass of 24 grams. If sphere A has a density of 12 g/mL and sphere B has a density of 3 g/mL. What can you conclude about the volume of each?

It has been concluded that the volume of sphere A has been 4 times greater than the volume of sphere B.

Density can be defined as the mass per unit volume. Density can be expressed as:

Density =

Sphere A has a mass of 24 grams, and a density of 12 g/ml.

Sphere B has a mass of 24 grams and a density of 3 g/ml.

Since the spheres have the same mass, the relationship can be given as:

Density of A × Volume of A = Density of B × Volume of B

12 × Volume of A = 3 × Volume of B

4 × Volume of A = Volume of B

Thus, it has been concluded that the volume of sphere A has been 4 times greater than the volume of sphere B.

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Volume of sphere A = 2 mL

Volume of sphere B = 8 mL

The volume of sphere B is 4 times the volume of sphere A.

Explanation:

We'll begin by calculating the volume of each sphere.

Data obtained from the question include:

Sphere A:

Mass = 24 g

Density = 12 g/mL

Volume =?

Sphere B:

Mass = 24 g

Density = 3 g/mL

Volume =?

Next, we shall determine the volume of each sphere. This can be obtained as follow:

For sphere A:

Density = mass /volume

12 = 24/volume

Cross multiply

12 × volume = 24

Divide both side by 12

Volume = 24/12

Volume = 2 mL

For sphere B:

Density = mass /volume

3 = 24/volume

Cross multiply

3 × volume = 24

Divide both side by 3

Volume = 24/3

Volume = 8 mL

Summary:

Volume of sphere A = 2 mL

Volume of sphere B = 8 mL

Comparing the volume of both sphere, we have:

Va /Vb = 2/8

Va /Vb = 1/4

Cross multiply

Va × 4 = Vb

Vb = 4Va

From the above illustration,

The volume of sphere B is 4 times the volume of sphere A.

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