Density, Mass and Volume

Density tells you the mass of each cubic centimetre.

Divide the mass by the volume.

Each cubic centimetre of the plastic has a mass of 1.2 g.

Work out how many lots of 19 g there are in the mass.

The answer is in grams per cm³, so change the mass into grams first.

Divide the mass by the volume, then round.

1. Density = mass ÷ volume =250\div28=8.928...
2. To 1 decimal place, the density is 8.9 g/cm³.

Work out the volume of the cuboid first.

1. Volume =5\times3\times4=60 cm³.
2. Density = mass ÷ volume =150\div60=2.5 g/cm³.

Find the volume of the candle, then use mass = density × volume.

1. Volume =8\times5\times2=80 cm³.
2. Mass = density × volume =0.9\times80=72 g.

Work out the mass in grams first, then change it into kilograms.

1. Mass =7.8\times4500=35\,100 g.
2. 35\,100\div1000=35.1, so the mass is 35.1 kg.

Work out the density of each block.

1. Block A: 540\div200=2.7 g/cm³.
2. Block B: 324\div120=2.7 g/cm³.
3. The densities are equal, so both blocks have the same density, even though A is heavier.

The volume of a prism is the area of its cross-section times its length.

1. Area of the triangle =\frac{1}{2}\times8\times3=12 cm².
2. Volume =12\times15=180 cm³.
3. Mass =1.4\times180=252 g.

The volume of a cylinder is \pi r^2h. Use the radius, not the diameter.

1. Radius =12\div2=6 cm.
2. Volume =\pi\times6^2\times5=180\pi=565.48... cm³.
3. Density =620\div565.48...=1.0964...
4. To 3 significant figures, the density is 1.10 g/cm³.

Find the mass of one block in kilograms.

1. Mass of one block =2.3\times9000=20\,700 g =20.7 kg.
2. 750\div20.7=36.23...
3. The lift can carry 36 whole blocks (37 blocks would be more than 750 kg).

Use the mass and density to find the volume first.

1. Volume = mass ÷ density =486\div2.7=180 cm³.
2. Length × width =10\times4=40 cm².
3. Height =180\div40=4.5 cm.

The piece is made of the same metal, so it has the same density as the whole bar.

1. 2.4 kg =2400 g, so the density is 2400\div300=8 g/cm³.
2. Mass of the piece =8\times45=360 g.

Find the total mass and the total volume of the drink.

1. Volume of syrup =200\div1.25=160 cm³.
2. Mass of water =1\times340=340 g.
3. Total mass =200+340=540 g. Total volume =160+340=500 cm³.
4. Density of the drink =540\div500=1.08 g/cm³.

Use the oil to find how much the jar holds.

1. Volume of the jar =1380\div0.92=1500 cm³.
2. Mass of honey =1.4\times1500=2100 g.
3. 2100 g =2.1 kg.

Density = mass ÷ volume for each solid.

Part (a)

1. Volume of P =5\times5\times5=125 cm³.
2. Density of P =1000\div125=8 g/cm³.

Part (b)

1. Volume of Q =4\times3\times2=24 cm³, so the density of Q is 72\div24=3 g/cm³.
2. Density of P : density of Q =8:3.

Find the mass of each part separately, then add.

1. Volume of the base =10\times8\times3=240 cm³, so its mass is 0.75\times240=180 g.
2. Volume of the cube =4\times4\times4=64 cm³, so its mass is 8.5\times64=544 g.
3. Total mass =180+544=724 g.

Find the volume in cm³, then the mass of sand in kilograms.

1. Volume =2\times1.5\times0.3=0.9 m³ =900\,000 cm³.
2. Mass of sand =1.6\times900\,000=1\,440\,000 g =1440 kg.
3. 1440\div25=57.6
4. Jo can only buy whole bags, so she needs 58 bags.