Question

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

Answer 1

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


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


$= 340c {m}^{3}$

Answer 2

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

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https://brainly.com/question/11168779