The dimensions of a large room are double the dimensions of a small room. Both rooms are rectangular prisms. The volume of the small room is 10 cubic meters. What is the volume of the large room?
Answer (3)
Volume id proportional to the cube of the dimensions.
The volume of the larger room is 10 x (2 cubed) = 80 cubic metres.
The student is working with concepts related to the volume of rectangular prisms, particularly how changing dimensions affect volume. We are given that a small room has a volume of 10 cubic meters, and a large room has dimensions that are double those of the small room. To calculate the volume of the large room, we consider that volume is proportional to the cube of the linear dimensions. If the linear dimensions are doubled, then the new volume will be 23, or 8 times the original volume.
Therefore, the volume of the large room is 10 cubic meters × 8, which equals 80 cubic meters.
The volume of the large room is 80 cubic meters, which is calculated by recognizing that it has dimensions double that of the small room. Since volume scales with the cube of the dimensions, the volume of the large room is 8 times that of the small room. Given that the small room has a volume of 10 cubic meters, the large room's volume is 80 cubic meters.
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