Question

the cross section of rectangular prism a measures 6 units by 4 units. the cross section of triangular prism b has a base that measures 8 units and a height of 6 units. if the length of each prism is 7.22 units, which statement is true?
volume a = \\( \frac { 1 } { 2 } \\) (volume b)
volume a = 2(volume b)
volume a = \\( \frac { 1 } { 3 } \\) (volume b)
volume a = volume b

Explanation:

Step1: Calculate the area of the cross - section of prism A

The cross - section of prism A is a rectangle. The area formula for a rectangle is \(A = l\times w\). Given \(l = 6\) units and \(w = 4\) units, so \(A_{A}=6\times4 = 24\) square units.

Step2: Calculate the area of the cross - section of prism B

The cross - section of prism B is a triangle. The area formula for a triangle is \(A=\frac{1}{2}\times b\times h\). Given \(b = 8\) units. Let's assume the height of the triangle (using the fact that the prisms have the same "slant" height of 6 units in a sense related to the volume formula \(V=A\times h\) where \(h\) is the length of the prism). The area of the triangle \(A_{B}=\frac{1}{2}\times8\times6= 24\) square units. But wait, no, the formula for the volume of a prism is \(V = A\times l\) (where \(A\) is the area of the cross - section and \(l\) is the length of the prism).
The correct formula: For prism A (rectangular prism), \(V_{A}=A_{A}\times l\), where \(A_{A}=6\times4\) (area of the rectangular cross - section) and \(l = 7.22\). For prism B (triangular prism), \(A_{B}=\frac{1}{2}\times8\times6\) (area of the triangular cross - section) and \(l = 7.22\)
\(V_{A}=(6\times4)\times7.22\) and \(V_{B}=(\frac{1}{2}\times8\times6)\times7.22\)
\(V_{A}=24\times7.22\) and \(V_{B}=24\times7.22\)

Answer:

Volume \(A=\) Volume \(B\)