Question

select all the true statements about a rectangular prism. a. a rectangular prism is a solid figure with 6 rectangular faces. b. a rectangular prism is composed of layers that look different. c. each layer in a rectangular prism is made up of rows and columns. d. the volume of a rectangular prism can only be determined by counting every unit cube. e. rectangular prisms that look different may have the same volume.

Explanation:

• Option A: A rectangular prism (also called a cuboid) has 6 faces, and all faces are rectangles (in a right rectangular prism; in some cases, two faces can be squares, but squares are special rectangles), so this is true.
• Option B: In a rectangular prism, the layers (if we think of it as stacked unit cubes or layers of the same cross - section) should look the same. For example, if the base is a rectangle with length \( l \) and width \( w \), each layer parallel to the base will have the same \( l \) and \( w \), so this statement is false.
• Option C: Each layer (a cross - sectional layer) of a rectangular prism, when considered as a 2 - D figure, is a rectangle which can be thought of as being made up of rows and columns of unit squares (or the basic units of the layer), so this is true.
• Option D: The volume of a rectangular prism can be calculated using the formula \( V=l\times w\times h \) (where \( l \) is length, \( w \) is width, and \( h \) is height) instead of just counting unit cubes, so this statement is false.
• Option E: For example, a rectangular prism with \( l = 2\), \( w=3\), \( h = 4\) has a volume of \( 2\times3\times4 = 24\), and another rectangular prism with \( l = 1\), \( w = 6\), \( h=4\) also has a volume of \( 1\times6\times4=24\) but they look different, so this statement is true.

Answer:

A. A rectangular prism is a solid figure with 6 rectangular faces.
C. Each layer in a rectangular prism is made up of rows and columns.
E. Rectangular prisms that look different may have the same volume.