# Z varies inversely as the cube of d. If z = 3 when d = 2, how do you find z when d is 4?

Jun 1, 2017

$z = \frac{3}{8}$

#### Explanation:

$z$ varies inversely as the cube of $d$ means $z \propto \frac{1}{d} ^ 3$

In other words $z = k \times \frac{1}{d} ^ 3$, where$k$ is a constant.

Now as $z = 3$ when $d = 2$ means

$3 = k \times \frac{1}{2} ^ 3$ or $3 = k \times \frac{1}{8}$ or $k = 8 \times 3 = 24$

Hence $z = 24 \times \frac{1}{d} ^ 3 = \frac{24}{d} ^ 3$

Therefore when $d = 4$,

$z = 24 \times \frac{1}{4} ^ 3 = \frac{24}{64} = \frac{3}{8}$.