Problem Solving with Volumes Flashcards

All 7 cards in this deck

How many cm$^3$ and how many ml are there in $1$ litre?

$1$ litre $= 1000$ cm$^3 = 1000$ ml (so $1$ ml $= 1$ cm$^3$)

True or false? $1$ m$^3 = 100$ cm$^3$.

False. $1$ m$^3 = 100 \times 100 \times 100 = 1\,000\,000$ cm$^3$.

What are the steps to find the volume of a composite solid?

e.g. a cuboid $5$ cm $\times$ $4$ cm $\times$ $2$ cm with a cube of side $2$ cm on top

1. Split the solid into simple solids: cuboid + cube
2. Find each volume: $5 \times 4 \times 2 = 40$ and $2^3 = 8$
3. Add them: $40 + 8 = 48$ cm$^3$

What are the steps to find how many cups can be completely filled from a partly full container?

e.g. a container of volume $3420$ cm$^3$ that is $\frac{2}{3}$ full, cups of $275$ ml

1. Volume of water: $3420 \times \frac{2}{3} = 2280$ cm$^3$ ($= 2280$ ml)
2. Divide by the cup capacity: $2280 \div 275 = 8.29...$
3. Round down: $8$ cups

When a volume calculation for how many whole boxes fit into a container gives a decimal answer, what do you do with it?

Round down to the whole number below — a part box does not count.

What are the steps to decide whether a claim about a volume is correct, showing your working?
e.g. Vera says 6 cubes of side $2$ cm have a total volume of $48$ cm$^3$

1. Work out the volume of one solid: $2 \times 2 \times 2 = 8$ cm$^3$
2. Scale up or combine as the claim describes: $8 \times 6 = 48$ cm$^3$
3. Compare with the claim and write a conclusion: $48 = 48$, so Vera is correct

True or false? Doubling the edge length of a cube doubles its volume.

False.
All three dimensions double, so the volume becomes $2 \times 2 \times 2 = 8$ times larger.