Question

A graduated cylinder contains 62 ml of water. When a small metal block is added to the water, the volume of the water increases to 65.5 ml. If the block is 26g, what is the density

Answer 1

7.43 g/mL

Step-by-step explanation:

Step 1:

Data obtained from the question. This include:

Volume of water = 62 mL

Volume of (Metal + water) = 65.5 mL

Mass of metal = 26g

Density =?

Step 2:

Determination of the volume of the block.

From Archimedes' principle, we understood that an object will displace its own volume when completely immersed in a liquid. The volume of the metal block can be obtained as follow:

Volume of water = 62 mL

Volume of (Metal + water) = 65.5 mL

Volume of the matal = Volume of (Metal + water) - volume of water

Volume of the matal = 65.5 - 62

Volume of the matal = 3.5 mL

Step 3:

Determination of the density of the metal block. This is illustrated below:

The density of an object is simply the mass of the object per unit volume of the object. It represented mathematically as:

Density = Mass /volume

Mass of the metal = 26g

Volume of the metal = 3.5 mL

Density =?

Density = Mass /volume

Density = 26g / 3.5mL

Density = 7.43 g/mL

Answer 2

The density of the block is 7.4g/ml.

Step-by-step explanation:

We can determine the volume of the metal block by taking the difference between the volumes measured in the graduated cylinder:

`V_(block)=65.5ml-62ml\\\\V_(block)=3.5ml`

Now, as we know that the average density of an object is calculated dividing its mass by its volume, we can calculate the density ρ of the metal block using the expression:

`\rho_(block)=(m_(block))/(V_(block))\\\\\rho_(block)=(26g)/(3.5ml)\\\\\rho_(block)=7.4(g)/(ml)`

Finally, it means that the density of the metal block is 7.4g/ml.