More Difficult Problems (Leaving Cert Mathematics): Flashcards

Volume of liquid passing through pipe per unit time

$\pi r^2 \times \text{flow speed (cm/sec)}$

Vol. of pipe segment, length = flow speed

Total volume ÷ volume per second

$a^3:b^3$

Volume has 3 dimensions, each contributes to scaling

$V = \pi r^2 h$

$V = \frac{1}{3}\pi r^2 h$

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

$V = \frac{2}{3}\pi r^3$

Combinations of basic 3D shapes

Break down into familiar basic components

Add components; subtract hollow inner volumes

1000 cm³