To find the minimum number of identical containers Rene would need to make 2,000 cm³ of ice, we first need to calculate the volume of one container, which is in the shape of a cylinder.
The formula for the volume \( V \) of a cylinder is given by:
\[ V = \pi r^2 h \]
Where:
- \( r \) is the radius of the base.
- \( h \) is the height of the cylinder.
- Calculate the radius: The diameter of the base is 6 cm, so the radius \( r \) is:
\[ r = \frac{6 \text{ cm}}{2} = 3 \text{ cm} \]
- Substitute values into the volume formula: The height \( h \) is 8 cm. Now plug in the values into the formula using \( \pi = 3.14 \):
\[ V = 3.14 \times (3 \text{ cm})^2 \times 8 \text{ cm} \]
- Calculate the squared radius:
\[ (3 \text{ cm})^2 = 9 \text{ cm}^2 \]
- Calculate the volume:
\[ V = 3.14 \times 9 \text{ cm}^2 \times 8 \text{ cm} = 3.14 \times 72 \text{ cm}^3 = 226.08 \text{ cm}^3 \]
- Find the number of containers needed:
To find how many containers are needed to make 2,000 cm³ of ice, we divide the total volume needed by the volume of one container:
\[ \text{Number of containers} = \frac{2000 \text{ cm}^3}{226.08 \text{ cm}^3} \]
Calculating this gives:
\[ \text{Number of containers} \approx 8.84 \]
Since we can't have 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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