Question

Three blocks are shown:

Which statement is correct? (1 point)

a
Block A has the greatest density.

b
Block B has the greatest density.

c
The density of Block A is equal to the density of Block B.

d
The density of Block B is equal to the density of Block C.

Answer 1

Answer: Block A has the greatest density.

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Step-by-step explanation:

We'll need the volume of each block.

To find the volume, multiply length width and height together.

• Block A volume = 6*4*2 = 48 cubic cm
• Block B volume = 6*2*4 = 48 cubic cm
• Block C volume = 2*4*6 = 48 cubic cm

All three blocks have the same volume even though they look different. This is because the order of the 2, 4 and 6 doesn't matter. The blocks are just rotated versions of one another.

Divide the mass of the block over the volume to find the density.

• Block A density = (mass)/(volume) = (3 kg)/(48 cubic cm) = 0.0625 kg per cubic cm
• Block B density = (mass)/(volume) = (1 kg)/(48 cubic cm) = 0.0208333 kg per cubic cm (approximate)
• Block C density = (mass)/(volume) = (2 kg)/(48 cubic cm) = 0.041667 kg per cubic cm (approximate)

To summarize, we have these densities:

• Block A = 0.0625 kg per cubic cm (exact)
• Block B = 0.0208333 kg per cubic cm (approximate)
• Block C = 0.0416667 kg per cubic cm (approximate)

We then see that block A has the greatest density since 0.0625 is the largest among the three results. More material is packed in the same volume of space compared to the other blocks. In other words, its more densely packed.

You can think of a crowded city being dense with people, compared to a wide open rural town that has fewer people and is less dense.

Possibly the quickest way to see how or why block A is the most dense is to notice block A has the most mass. The more mass, the higher the density when we fix the volume to be the same each time. Therefore, block B will be the least dense since it has the lowest mass. Once again, this trick only works when the volumes are all the same. Otherwise, you'll have to compute the densities shown above.

Answer 2

a

Block A has the greatest density.

Step-by-step explanation:

All the options are comparing density of blocks, therefore, let's find the density of all the blocks and compare their values.

Remember that the formula for density is:
`d=(mass)/(volume)`.

1. Density of Block A.

Mass= 3 kg. It's preferable to use mass as grams for a density scale, let's convert the kg to g by multiplying by 100:

`3kg*1000=3,000g`.

Volume. We are looking for the volume of a rectangular prism. Formula:
`V=lwh`. Where l is the length of the prism, w is its width and h is the height.

`V=(2cm)(6cm)(4cm)=48cm^(3)`

`d=(3000g)/(48cm^(3) ) =62.50g/cm^{3`

2. Density of Block B.

Mass:
`1kg*1000=1000g`.

Volume:
`(4)(6)(2)=48cm^(3)`

`d=(1000g)/(48cm^(3) ) =20.83g/cm^{3`

3. Density of Block C.

Mass:
`2kg*1000=2000g`.

Volume:
`(4)(2)(6)=48cm^(3)`

`d=(2000g)/(48cm^(3) ) =41.67g/cm^{3`

4. Compare all the densities.

Block A:
`62.50g/cm^{3`

Block B:
`20.83g/cm^{3`

Block C:
`41.67g/cm^{3`

5. Select the correct answer.

a

Block A has the greatest density.

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This problem could've been solved without making any calculations, since the dimensions of all blocks is the same, but their mass is different. Knowing that density is mass/volume, and taking into acount that the volume is always the same, the block with the highest mass is the one with the highest density aswell.