Question: The cylindrical jar below is filled with water at a rate of $20$ ml per second.
Work out how long it will take to completely fill the jar.
Give your answer to the nearest second.
$1$ ml = $1$ cm$^3$
$4$ cm
$9$ cm
position_hint: center
Cylinder diagram in the lower center: a cylindrical jar with a horizontal radius label of $4$ cm at the top left of the jar and a vertical height label of $9$ cm on the right side.
1. **State the problem:** We need to find how long it takes to fill a cylindrical jar with water flowing at $20$ ml per second.
2. **Given:** Radius $r = 4$ cm, Height $h = 9$ cm, Flow rate $= 20$ ml/s, and $1$ ml $= 1$ cm$^3$.
3. **Formula for volume of a cylinder:**
$$V = \pi r^2 h$$
4. **Calculate the volume:**
$$V = \pi \times 4^2 \times 9 = \pi \times 16 \times 9 = 144\pi \text{ cm}^3$$
5. **Convert volume to ml:** Since $1$ ml $= 1$ cm$^3$, volume $= 144\pi$ ml.
6. **Calculate time to fill:**
$$\text{time} = \frac{\text{volume}}{\text{flow rate}} = \frac{144\pi}{20} = \frac{144}{20}\pi = 7.2\pi \text{ seconds}$$
7. **Approximate the time:**
$$7.2 \times 3.1416 \approx 22.62 \text{ seconds}$$
8. **Round to nearest second:**
$$23 \text{ seconds}$$
**Final answer:** It will take approximately **23 seconds** to fill the jar completely.