Question

question 5 (multiple choice worth 2 points)
(06 01 mc)
the cross section of rectangular prism a measures 3 units by 2 units. the cross section of triangular prism b has a base that measures 4 units and a height of 3 units. if the length of each prism is 3.6 units, which statement is true?
volume a = volume b
volume a = 1/2 (volume b)
volume a = 2(volume b)
volume a = 1/3 (volume b)

Explanation:

Step1: Calculate Volume of Prism A

Prism A is a rectangular prism. The formula for the volume of a rectangular prism is \( V = l \times w \times h \), where \( l \) is length, \( w \) is width, and \( h \) is height. The cross - section (base) has dimensions 3 units by 2 units, and the length of the prism is 3.61 units. So, \( V_A=3\times2\times3.61 = 21.66 \) cubic units.

Step2: Calculate Volume of Prism B

Prism B is a triangular prism. The formula for the volume of a triangular prism is \( V=\frac{1}{2}\times b\times h_{triangle}\times l_{prism} \), where \( b \) is the base of the triangle, \( h_{triangle} \) is the height of the triangle, and \( l_{prism} \) is the length of the prism. The base of the triangular cross - section is 4 units, the height of the triangle is 3 units, and the length of the prism is 3.61 units. So, \( V_B=\frac{1}{2}\times4\times3\times3.61= 21.66 \) cubic units.

Answer:

Volume A = Volume B