Respuesta :

IsrarAwan
Given data:

Volume of the prism A = 2080 [tex]c m^{3} [/tex]

Let us find the ratio of the volume of prisms given in the diagram:
[tex] \frac{ V_{A}}{V_{B}} = \frac{8^{3}}{4^{3}} [/tex]
[tex] \frac{ V_{A}}{V_{B}} = 8 [/tex]


Since the condition is:
The volume of Prism A = The volume of Prism B
Therefore,
The ratio of their volumes should be 8.
[tex] \frac{ V_{A}}{V_{B}} =8 [/tex]

Since Volume of A = 2080 [tex]cm^{3} [/tex]

Plug-in the value, you would get:

[tex] \frac{2080}{8}} = V_{B}[/tex]

Ans: Volume of B = 260 [tex]cm^{3} [/tex]

The volume of prism B is [tex]\rm 260 \; cm^3[/tex] and this can be determined by taking the ratio of the volume of both the prism.

Given :

  • Prism A is similar to Prism B.
  • The volume of Prism A is 2080 cm³.

To determine the volume of prism B, first determine the ratio of the volume of prism A to the volume of prism B that is:

[tex]\rm \dfrac{V_A}{V_B}=\dfrac{8^3}{4^3}[/tex]

[tex]\rm \dfrac{V_A}{V_B}=8[/tex]

Now, put the value of the volume of prism A in the above expression.

[tex]\rm \dfrac{2080}{V_B} = 8[/tex]

Divide 2080 by 8 in the above equation.

[tex]\rm V_B = \dfrac{2080}{8}[/tex]

[tex]\rm V_B = 260\;cm^3[/tex]

So, the volume of prism B is [tex]\rm 260 \; cm^3[/tex].

For more information, refer to the link given below:

https://brainly.com/question/15861918

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