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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.
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 !
To describe the faces of the right rectangular prism, we can examine the cross sections formed by the horizontal and vertical planes.
1. Horizontal Cross Section: This cross section forms a rectangle with dimensions 8 inches and 12 inches. Since it is a cross section "horizontally," these dimensions represent the length and width of the base of the prism.
2. Vertical Cross Section: This cross section forms a rectangle with dimensions 5 inches and 8 inches. In this case, the dimensions represent the height and width of the prism.
Based on these observations, we can conclude that the prism has a length of 8 inches, a width of 12 inches, and a height of 5 inches.
To find the volume of the prism, we can use the formula:
Volume = Length × Width × Height
Plugging in the values we determined, we have:
Volume = 8 inches × 12 inches × 5 inches
Calculating this expression, we get:
Volume = 480 cubic inches
Therefore, the volume of the right rectangular prism is 480 cubic inches.