Question

question 1
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 3.61 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 Volume of Prism A

The volume of a rectangular prism is given by the formula \( V = \text{length} \times \text{width} \times \text{height} \) (or for cross - section, \( V=\text{area of cross - section}\times\text{length of prism} \)). The cross - section of prism A is a rectangle with dimensions 3 units and 2 units, and the length of the prism is 3.61 units. So the area of the cross - section of A, \( A_A=3\times2 = 6\) square units. Then the volume of A, \( V_A=A_A\times l=6\times3.61 = 21.66\) cubic units.

Step2: Calculate Volume of Prism B

The volume of a triangular prism is given by the formula \( V=\text{area of triangular cross - section}\times\text{length of prism} \). The area of a triangle is \( A=\frac{1}{2}\times\text{base}\times\text{height} \). For prism B, the base of the triangular cross - section is 4 units and the height is 3 units. So the area of the triangular cross - section, \( A_B=\frac{1}{2}\times4\times3=6\) square units. The length of the prism is 3.61 units. Then the volume of B, \( V_B = A_B\times l=6\times3.61=21.66\) cubic units.

Step3: Compare the Volumes

We have calculated that \( V_A = 21.66\) and \( V_B=21.66 \). So \( V_A = V_B \).

Answer:

Volume A = Volume B