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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? 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).

Respuesta :

Volume of an object is the measure of the space that object occupies. The correct comparison of volume of considered objects is: Volume of A = Volume of B

How to find the volume of a right rectangular prism?

Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:

[tex]V = a\times b \times c \: \rm unit^3[/tex]

How to find the volume of right triangular prism?

It can be obtained by multiplying the cross sectional triangle's area to the height of the considered triangular prism.

Thus, for the given case, we get:

  • Volume of rectangular prism:

Its dimensions are 1.5 units by 1 units by 1.81 units

Thus, [tex]V_A = 1.5 \times 1 \times 1.81 = 1.5 \times 1.81 = 2.715 \: \rm unit^3[/tex]

  • Volume of triangular prism:

Its cross section triangle has base of 2 units and height of 1.5 unit. The height of the prism is equal to the height of the considered rectangular prism = 1.81 units,

Thus,

[tex]V_B = \text{Area of triangular cross-section} \times 1.81 = \dfrac{1}{2} \times 2\times 1.5 \times 1.81 \: \rm unit^3\\V_B = 2.715\: \rm unit^3\\\\[/tex]

Thus, we get [tex]V_A = V_B[/tex]((Volume of A = Volume of B)

Learn more about volume of triangular prism here:

https://brainly.com/question/8565162

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