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?

Question

rectangular prism A , with a cross-section that is parallel to its respective basetriangular prism B, with a cross-section that is parallel to its respective base

Volume B = one half(Volume A)
Volume B = one third(Volume A)
Volume B = Volume A
Volume B = 2(Volume A)

Answer 1

To compare the volumes of the two prisms, we need to calculate the volume of rectangular prism A and triangular prism B.

Volume of Rectangular Prism A:

The volume \( V_A \) of a rectangular prism can be calculated using the formula:

\[ V_A = \text{Base Area} \times \text{Height} \]

For prism A:

• Base Area = Length × Width = \( 1.5 , \text{units} \times 1 , \text{unit} = 1.5 , \text{square units} \)
• Height = 1.81 units

So, the volume of prism A is:

\[ V_A = 1.5 , \text{square units} \times 1.81 , \text{units} = 2.715 , \text{cubic units} \]

Volume of Triangular Prism B:

The volume \( V_B \) of a triangular prism can be calculated using the formula:

\[ V_B = \text{Base Area} \times \text{Height} \]

For prism B:

• Base Area of the triangle = \( \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2 , \text{units} \times 1.5 , \text{units} = 1.5 , \text{square units} \)
• Height = 1.81 units

So, the volume of prism B is:

\[ V_B = 1.5 , \text{square units} \times 1.81 , \text{units} = 2.715 , \text{cubic units} \]

Comparison of Volumes:

• \( V_A = 2.715 , \text{cubic units} \)
• \( V_B = 2.715 , \text{cubic units} \)

Since both volumes are equal:

\[ V_B = V_A \]

Therefore, the correct statement is:

Volume B = Volume A.