Question

Find the density of a block with a length of 8.0 cm, a width of

4.0 cm, a height 2.0 cm, and a mass of 32 g. Would this block
float or sink in water?

Answer 1

d= 0.5 g/ cm³

The block will float in water.

Step-by-step explanation:

The density of an object can be found using the following formula:

`d=(m)/(v)`

where
`m` is the mass and
`v` is the volume. We know the block has a mass of 32 grams. We don't know the volume, therefore we must calculate it.

Let's assume the block is a cube. The volume of a cube can be found using the following formula.

`v=l*w*h`

The length is 8 cm, the width is 4 cm and the height is 2 cm.

`l= 8 cm \\w= 4cm \\h= 2cm`

`v= 8 cm * 4 cm * 2cm`

`v=32 cm^2 * 2cm`

`v= 64 cm^3`

Now we know the volume and can substitute it into the formula, along with the mass.

`d=(m)/(v)`

`m= 32 g\\v= 64 cm^3`

`d=(32 g)/(64 cm^3)`

Divide 32 grams by 64 cubic centimeters.

`d= 0.5 g/cm^3`

The density of the block is 0.5 grams per cubic centimeter. The density of water is 1.0 g/cm³. Any object with a density that is less than 1 will float in water. 0.5 is less than 1, so this object will float in water.

Answer 2

Density = 0.5 g/cm³

Step-by-step explanation:

Density of a substance can be found by using the formula

`Density = (mass)/(volume)`

From the question

mass = 32g

To find the density we must first find the volume of the block

From the question the block is a cuboid

Volume of cuboid = length × width × height

length = 8 cm

width = 4 cm

height = 2 cm

Volume of block = 8 × 4 × 2 = 64 cm³

Substitute the values into the above formula and solve for the density

That's....

`Density = (32)/(64) \\ = (1)/(2)`

We have the final answer as

Density = 0.5 g/cm³

The block will float because it's density is less than the density of water which is

1 g/cm³

Hope this helps you