Question

write the steps
there are two water planter globes. globe a has a diameter of 3 inches
and it takes 9 days to drain, whereas globe b has a diameter of 4 inches.
how long will it take globe b to drain?
your answer

Explanation:

Step1: Find the radius of each globe

Radius of Globe A: $r_A=\frac{3}{2}=1.5$ inches.
Radius of Globe B: $r_B = \frac{4}{2}=2$ inches.

Step2: Use the relationship between volume and time (assuming volume - time proportionality, volume of a sphere $V=\frac{4}{3}\pi r^{3}$)

Let $t_A = 9$ days (time for Globe A to drain), $V_A=\frac{4}{3}\pi r_A^{3}$, $V_B=\frac{4}{3}\pi r_B^{3}$.
Since $\frac{V_A}{t_A}=\frac{V_B}{t_B}$ (rate of draining is assumed constant), and $V\propto r^{3}$, we have $\frac{r_A^{3}}{t_A}=\frac{r_B^{3}}{t_B}$.
Substitute $r_A = 1.5$, $r_B=2$, $t_A = 9$ into $\frac{r_A^{3}}{t_A}=\frac{r_B^{3}}{t_B}$:
$\frac{(1.5)^{3}}{9}=\frac{(2)^{3}}{t_B}$.

Step3: Solve for $t_B$

Cross - multiply: $(1.5)^{3}\times t_B=9\times(2)^{3}$.
Calculate $(1.5)^{3}=3.375$ and $(2)^{3}=8$.
So, $3.375t_B=9\times8 = 72$.
Then $t_B=\frac{72}{3.375}=21.33\cdots=\frac{64}{3}\approx21.33$ days.

Answer:

It will take Globe B approximately $\frac{64}{3}\approx21.33$ days to drain.