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Answered

Prism A is similar to Prism B. The volume of Prism A is 2720 cm³.




What is the volume of Prism B?



A.21,760 cm³


B.1360 cm³


C.680 cm³


C.340 cm³

Prism A is similar to Prism B. The volume of Prism A is 2720 cm . What is the volume of Prism B? A.21,760 cm B.1360 cm C.680 cm C.340 cm class=

Verified Answer :

kudzordzifrancis

ANSWER


340 cm³


EXPLANATION


From the diagram we can determine the scale factor for the sides of the prisms.


Taking prism A to be the object and prism B to be the image,


The scale factor is


\(k = \frac{4}{8} = \frac{1}{2}\)




The scale factor for the volume is

\({k}^{3} = \frac{1}{8}\)


Since the volume of prism A is 2720cm³, we multiply this by the scale factor of the volume to get the volume of prism B.




Volume of prism B is


\(= \frac{1}{8} \times 2720c {m}^{3}\)


\(= 340c {m}^{3}\)

Volume for Prism B = 340 cm³

Given

Prism A is similar to Prism B.

From figure

Length of one side of Prism A  = 8 cm

Length of one side of Prism B =  4 cm

The volume of Prism A is 2720 cm³.

The scale factor is defined as given below

Let the scale factor be represented as S

\(\rm S = Scale \; factor = \dfrac{Final \; Length }{Initial \; Length } \\S = Scale \; factor = \dfrac{4 }{8 } = \dfrac{1}{2} \\\)

The scale factor for volume of the given prism  can be given  as \(\rm \bold{S^3}\)

So the scale factor for given prism

\(\rm Scale \; factor\; for \; the \; given \; prism = (1/2)^3 = \dfrac{1}{8}\)

Volume of Prism A = 2720 \(\rm {cm}^3\)

So the Volume for Prism B can be calculated as

\(\rm(Volume \; of\; Prism \; A ) \times \bold S = \dfrac{2720 }{8} = 340 \; {cm} ^3\)

Volume for Prism B = 340 cm³

For more information please refer to the link below

https://brainly.com/question/11168779

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