Find the volume of the oblique rectangular prism with length 9m, width 2m, and height 6m.
The correct answer and explanation is:
The volume of a rectangular prism is calculated using the formula: V=length×width×heightV = \text{length} \times \text{width} \times \text{height}
Given:
- Length = 9 m
- Width = 2 m
- Height = 6 m
Plugging the values into the formula: V=9 m×2 m×6 m=108 m3V = 9 \, \text{m} \times 2 \, \text{m} \times 6 \, \text{m} = 108 \, \text{m}^3
So, the volume of the oblique rectangular prism is 108 cubic meters.
Even though this is an oblique rectangular prism (where the sides are not necessarily perpendicular), the formula for the volume remains the same because the volume of a rectangular prism depends only on its length, width, and height, regardless of the angle between the sides. This formula assumes that the base of the prism forms a rectangle, and the height is the perpendicular distance between the base and the opposite face. The oblique nature of the prism does not affect the calculation of volume as long as the shape of the cross-section is still a rectangle.
In this case, since the base and the height are still aligned in such a way that the sides form a rectangular shape, we are able to use the standard formula for volume. If the prism were non-rectangular in cross-section, a different method would be needed.