Alright, let's solve this step-by-step to find the height of the Vaseline camphor jar.
1. Given Data:
- Capacity of the jar, [tex]\(V\)[/tex] = 400 ml
- Radius of the jar, [tex]\(r\)[/tex] = 4 cm
- Given [tex]\(\pi\)[/tex] = 3.14
- 1 cm³ = 1 ml
Since the capacity given is in ml, which is equivalent to cm³, we directly use 400 cm³ for the volume.
2. Formula to be used:
We need to find the height, [tex]\(h\)[/tex], using the formula:
[tex]\[ h = \frac{V}{\pi r^2} \][/tex]
3. Substitute the given values into the formula:
- [tex]\( V = 400 \)[/tex] cm³
- [tex]\( r = 4 \)[/tex] cm
- [tex]\(\pi = 3.14\)[/tex]
[tex]\[ h = \frac{400}{3.14 \times (4)^2} \][/tex]
4. Calculate [tex]\(r^2\)[/tex]:
[tex]\[ r^2 = (4)^2 = 16 \][/tex]
5. Calculate [tex]\(\pi r^2\)[/tex]:
[tex]\[ \pi \times r^2 = 3.14 \times 16 = 50.24 \][/tex]
6. Calculate the height [tex]\(h\)[/tex]:
[tex]\[ h = \frac{400}{50.24} \approx 7.9618 \][/tex]
7. Round the height to the nearest whole number:
[tex]\[ \text{Rounded height} \approx 8 \][/tex]
So, the height of the Vaseline camphor jar is approximately 8 cm.
