Question

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.

Answer 1

Scale factor 1/19, volume 65.6 in³

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

Answer 2

• Scale factor 1/19, volume 65.6 in³

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