To solve the problem of finding the depth of the milk when one liter is poured into a cylindrical container with a radius of 10 cm, we can follow these steps:
1. Conversion of Volume:
- First, we need to convert the volume of milk from liters to cubic centimeters because the radius is given in centimeters. We know that 1 liter is equal to 1000 cubic centimeters (cm³).
- Therefore, the volume of milk in cubic centimeters is:
[tex]\[
\text{Volume} = 1 \text{ liter} = 1 \times 1000 \text{ cm}^3 = 1000 \text{ cm}^3
\][/tex]
2. Formula for the Volume of a Cylinder:
- The volume [tex]\( V \)[/tex] of a cylinder is given by the formula:
[tex]\[
V = \pi r^2 h
\][/tex]
Here, [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height or depth of the milk in the cylinder.
3. Rearrange the Formula to Solve for Height:
- To find the height [tex]\( h \)[/tex], we can rearrange the formula:
[tex]\[
h = \frac{V}{\pi r^2}
\][/tex]
4. Substitute the Values and Calculate:
- Plug in the given values into the formula. The volume [tex]\( V \)[/tex] is 1000 cm³ and the radius [tex]\( r \)[/tex] is 10 cm:
[tex]\[
h = \frac{1000}{\pi \times 10^2}
\][/tex]
[tex]\[
h = \frac{1000}{\pi \times 100}
\][/tex]
[tex]\[
h = \frac{1000}{100\pi}
\][/tex]
[tex]\[
h = \frac{10}{\pi}
\][/tex]
5. Calculate the Exact Depth:
- Using the value of [tex]\(\pi \approx 3.14159\)[/tex],
[tex]\[
h = \frac{10}{3.14159} \approx 3.1830988618379066 \text{ cm}
\][/tex]
6. Round the Depth to One Decimal Place:
- Finally, we round the depth to one decimal place:
[tex]\[
\text{Depth} \approx 3.2 \text{ cm}
\][/tex]
So, the depth of the milk in the cylindrical container is approximately 3.2 cm.
