Problem Solving with Volumes Flashcards

All 5 cards in this deck

What are the steps to find a missing height when the volume of a prism is given?

e.g. volume $60\text{ cm}^3$, length $5$ cm, triangular cross-section of base $4$ cm

1. Volume $\div$ length = cross-section area: $60 \div 5 = 12\text{ cm}^2$
2. Put this into the area formula: $\frac{1}{2}\times 4 \times h = 12$
3. Solve for $h$: $h = 6$ cm

What are the steps to find how long a container takes to fill at a given rate?

e.g. a tank of volume $6000\text{ cm}^3$ filled at $250\text{ cm}^3$ per second

1. Work out the volume of the container: $6000\text{ cm}^3$
2. Check the volume and the rate use the same units.
3. Time = volume $\div$ rate: $6000 \div 250 = 24$ seconds

What is the formula linking mass, density and volume of a solid?

mass = density $\times$ volume, so density = mass $\div$ volume.

True or false? When a solid is melted down and recast into a different shape, its volume stays the same.

True. So you can equate the two volumes to find a missing length.

True or false? The volume of a composite solid is always found by adding the volumes of the standard solids it can be split into.

False. If part of a solid has been removed (e.g. a drilled hole or the top of a cone), that volume is subtracted instead.