Question

The picture shows a container that Rene uses to freeze water:

A cylinder is shown with a base diameter of 6 centimeters and a height of 8 centimeters.

What is the minimum number of identical containers Rene would need to make 2,000 cm3 of ice? (Use π = 3.14.) (1 point)

27

9

3

2

Answer 1

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.

1. **Calculate the radius**:
The diameter of the base is 6 cm, so the radius \( r \) is:

\[
r = \frac{6 \text{ cm}}{2} = 3 \text{ cm}
\]

2. **Substitute values into the volume formula**:
The height \( h \) is 8 cm. Now plug in the values into the formula using \( \pi = 3.14 \):

\[
V = 3.14 \times (3 \text{ cm})^2 \times 8 \text{ cm}
\]

3. **Calculate the squared radius**:

\[
(3 \text{ cm})^2 = 9 \text{ cm}^2
\]

4. **Calculate the volume**:

\[
V = 3.14 \times 9 \text{ cm}^2 \times 8 \text{ cm} = 3.14 \times 72 \text{ cm}^3 = 226.08 \text{ cm}^3
\]

5. **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**.