Question

the cross - section of rectangular prism a measures 1.5 units by 1 unit. the cross - section of triangular prism b has a base that measures 2 units and a height of 1.5 units. if the length of each prism is 1.81 units, which statement is true? volume b = 2(volume a) volume b = volume a volume b = 1/3(volume a) volume b = 1/2(volume a)

Explanation:

Step1: Calculate volume of prism A

The volume formula for a prism is $V = Bh$, where $B$ is the area of the base and $h$ is the height. For rectangular - prism A, the cross - sectional area (base area) $B_A=1.5\times1 = 1.5$ square units and the height $h = 1.81$ units. So, $V_A=B_Ah=1.5\times1.81 = 2.715$ cubic units.

Step2: Calculate volume of prism B

For triangular - prism B, the cross - sectional area (base area) $B_B=\frac{1}{2}\times2\times1 = 1$ square unit and the height $h = 1.81$ units. So, $V_B=B_Bh=1\times1.81 = 1.81$ cubic units.

Step3: Find the ratio of volumes

Now, find the ratio $\frac{V_B}{V_A}=\frac{1.81}{2.715}=\frac{2}{3}$. So, $V_B=\frac{2}{3}V_A$.

Answer:

Volume B = $\frac{2}{3}$(Volume A)