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.)

27
9
3
2

Answer 1

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**.