A movie theatre sells popcorn in two sizes of rectangular prism containers.
The small container has a square base with 10 cm long sides and a height of 18 cm.
The large container has a square base with 12 cm long sides and a height of 21.6 cm.
Determine the factor by which the capacities of the two containers differ.
To determine the factor by which the capacities of the two containers differ, we need to find the volume of each container.
The volume of a rectangular prism is calculated by multiplying the length, width, and height of the prism.
For the small container:
Volume = side x side x height
Volume = 10 cm x 10 cm x 18 cm
Volume = 1800 cm³
For the large container:
Volume = side x side x height
Volume = 12 cm x 12 cm x 21.6 cm
Volume = 3110.4 cm³
To find the factor by which the capacities of the two containers differ, we divide the volume of the large container by the volume of the small container:
3110.4 cm³ / 1800 cm³ ≈ 1.728
Therefore, the factor by which the capacities of the two containers differ is approximately 1.728. This means that the large container has a capacity 1.728 times greater than the small container.