Volume Flashcards

All 8 cards in this deck

What is the formula for the volume of a cuboid?

$V = \text{length} \times \text{width} \times \text{height}$

e.g. $8 \times 5 \times 4 = 160$ cm$^3$

What are the steps to find a missing dimension of a cuboid from its volume?

e.g. volume $200$ cm$^3$, length $10$ cm, width $4$ cm — find the height

1. Multiply the two known dimensions: $10 \times 4 = 40$
2. Divide the volume by this: $200 \div 40 = 5$
3. Height $= 5$ cm

What is the formula for the volume of any right prism?

e.g. a triangular prism of cross-sectional area $6$ cm$^2$ and length $10$ cm

$V = \text{area of cross section} \times \text{length}$

$6 \times 10 = 60$ cm$^3$

What is the formula for the volume of a cylinder of radius $r$ and height $h$?

$V = \pi r^2 h$

e.g. $r = 3$, $h = 5$ gives $\pi \times 3^2 \times 5 = 45\pi$ cm$^3$

What is the formula for the volume of a sphere of radius $r$?

$V = \frac{4}{3}\pi r^3$

What is the formula for the volume of a pyramid or cone?

$V = \frac{1}{3} \times \text{base area} \times \text{perpendicular height}$

For a cone this gives $V = \frac{1}{3}\pi r^2 h$

What are the steps to find the volume of a cone when the formula is given in the question?
e.g. $V = \frac{1}{3}\pi r^2 h$ with $r = 3$ cm, $h = 10$ cm

1. Square the radius: $3^2 = 9$
2. Multiply by $\pi$ and by the height: $9 \times \pi \times 10 = 90\pi$
3. Multiply by $\frac{1}{3}$: $30\pi = 94.2$ cm$^3$ (3 s.f.)

A question gives the volume of a pyramid as $V = \frac{1}{3} \times \text{base area} \times \text{height}$. Which height must you substitute?
e.g. a square-based pyramid

The perpendicular (vertical) height from the base up to the apex.
Not the slant height along a sloping edge or face.