Volume Flashcards

All 8 cards in this deck

What is the formula for the volume of a prism?

e.g. a prism with cross-sectional area $12\text{ cm}^2$ and length $5$ cm

Volume = area of cross-section $\times$ length

$12 \times 5 = 60\text{ cm}^3$

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

$V = \pi r^2 h$

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 cone of base radius $r$ and height $h$?

$V = \frac{1}{3}\pi r^2 h$, where $h$ is the perpendicular (vertical) height, not the slant height.

What is the formula for the volume of a pyramid?

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

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

$1000\text{ cm}^3$, since $1\text{ cm}^3 = 1\text{ ml}$.

True or false? $1\text{ m}^3 = 100\text{ cm}^3$.

False. $1\text{ m}^3 = 1\,000\,000\text{ cm}^3$, since you multiply by $100$ for each of the three dimensions.

What are the steps to find the volume of a frustum of a cone?
e.g. a cone of radius $6$ cm and height $10$ cm with the top cone of radius $3$ cm and height $5$ cm removed

1. Volume of the full cone: $\frac13\pi\times6^2\times10=120\pi$
2. Volume of the small cone removed: $\frac13\pi\times3^2\times5=15\pi$
3. Subtract: $120\pi-15\pi=105\pi\text{ cm}^3$