To find out how many identical containers Rene needs to freeze 2,000 cm³ of water, we first need to calculate the volume of one cylindrical container.
The formula for the volume \( V \) of a cylinder is:
\[ V = \pi r^2 h \]
where:
- \( r \) is the radius of the base,
- \( h \) is the height.
Given:
- Diameter = 6 cm, therefore the radius \( r = \frac{6}{2} = 3 \) cm.
- Height \( h = 8 \) cm.
Now plug in the values:
\[ V = 3.14 \times (3)^2 \times 8 \] \[ V = 3.14 \times 9 \times 8 \] \[ V = 3.14 \times 72 \] \[ V = 226.08 \text{ cm}^3 \]
Now, we need to determine how many of these containers are needed to make 2,000 cm³ of ice.
To find the number of containers needed, divide the total volume of ice by the volume of one container:
\[ \text{Number of containers} = \frac{2000 \text{ cm}^3}{226.08 \text{ cm}^3} \] \[ \text{Number of containers} \approx 8.84 \]
Since we cannot use a fraction of a container, we round up to the nearest whole number:
\[ \text{Number of containers} = 9 \]
Thus, the minimum number of identical containers Rene would need to make 2,000 cm³ of ice is 9.
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