HELP!! Please scale a rectangular prism that is 300 inches, by 50 inches, by 30 inches to have a volume in the 60-70 cubic inch range.

Step-by-step explanation:

Volume of the prism:

Scaled volume is 60 - 70 in³

Find the scale factor k;

So the scale factor is

and the volume of the smaller prism is:

Scale factor 1/19, volume 65.6 in³

Step-by-step explanation:

Volume of the prism:

V = abh

V = 300*50*30 = 450000 in³

Scaled volume is 60 - 70 in³

Find the scale factor k;

450000/60 = 7500

450000/70 = 6428

1/6428 < 1/k³ < 1/7500

1/∛6428 < 1/∛k³ < 1/∛7500

1/18.59 < 1/k < 1/19.57

1/k = 19 is best

So the scale factor is

k = 1/19

and the volume of the smaller prism is:

450000 / 19³ = 65.6 in³

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