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If prism A and prism B have a ratio of similarity of 1:4, what is the volume of prism B if the
volume of prism A is 83 cubic units?

Respuesta :

benyjair

Answer:

Prism B = 332 Cubic Units

Step-by-step explanation:

"prism A and prism B have a ratio of similarity of 1:4"

1:4 is the same as  [tex]\frac{1}{4}[/tex] or [tex]\frac{A}{B}[/tex] this just means that A is 25% of B because 1/4=.25

that means that for A to = B you have to multiply A x 4

so A=83 we plug it into the equation and we get 83 x 4 = 332

A : B = 83 : 332

Answer:

Volume of Prism B: 5312 units^3

Step-by-step explanation:

  • we know that the ratio of prism A and prism B is 1:4
  • 1:4 is the same as 1/4
  • to find the volume ratio of similarity of the new figure you have to cube the ratio: 1/4^3 = 1/64
  • now that we know what the volume ratio is, we can now set up a table:

                          1/64=83/x           (x is B and 83 is A)

                          Cross multiply: 1·x

                                                    64·83

  • now we have an equation: 1x=5312
  • answer: V= 5312 units cubed

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