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.
2 answers:
Answer:
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
Answer:
- Scale factor 1/19, volume 65.6 in³
Step-by-step explanation:
<u>Volume of the prism:</u>
- V = abh
- V = 300*50*30 = 450000 in³
Scaled volume is 60 - 70 in³
<u>Find the scale factor k;</u>
- 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
<u>So the scale factor is </u>
<em>and the volume of the smaller prism is:</em>
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