A right rectangular prism is intersected by a horizontal plane and a vertical plane. The cross section formed by the horizontal plane and the prism is a rectangle with dimensions 8 inches and 12 inches. The cross section formed by the vertical plane and the prism is a rectangle with dimensions 5 inches and 8 inches. Describe the faces of the prism, including their dimensions. Then find its volume.
Thanks
12 by 8 by 5
five is the height because in vertical plane. 12 by 8 is the top and bottom.
Sketch a drawing of it !
Same question on my homework, the answer is 12x8x5, volume is 480.
To describe the faces of the prism, we can take a look at the dimensions of the rectangles formed by the intersection of the prism and the horizontal and vertical planes.
The first cross-section formed by the horizontal plane is a rectangle with dimensions 8 inches and 12 inches. Since this cross-section is parallel to the base of the prism, we can conclude that the base face of the prism has dimensions 8 inches and 12 inches.
The second cross-section formed by the vertical plane is a rectangle with dimensions 5 inches and 8 inches. Since this cross-section is perpendicular to the base of the prism and is non-parallel to any other face, we can determine that the side face of the prism has dimensions 5 inches and 8 inches.
Now let's find the volume of the prism. Since we know the dimensions of the base face (8 inches and 12 inches), we can use the formula for the volume of a rectangular prism: volume = length × width × height.
The height of the prism is the distance between the horizontal and vertical planes, which is equal to the length of the vertical cross-section, i.e., 5 inches.
Plugging in the values, we have volume = 8 inches × 12 inches × 5 inches. Multiplying these numbers gives us the volume of the prism:
volume = 480 cubic inches.
Therefore, the volume of the right rectangular prism is 480 cubic inches.