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26 May 2017, 04:43
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A certain cube has 150 inches as the length of one side. If the error of the length of one side is within 1 inch, what is the greatest possible difference between the actual volume and the estimated volume of the cube, in cubic inches?
A. 4,000
B. 7,000
C. 70,000
D. 140,000
E. 210,000
A. 4,000
B. 7,000
C. 70,000
D. 140,000
E. 210,000
26 May 2017, 04:45
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Bookmarks
Official Solution:
A certain cube has 150 inches as the length of one side. If the error of the length of one side is within 1 inch, what is the greatest possible difference between the actual volume and the estimated volume of the cube, in cubic inches?
A. 4,000
B. 7,000
C. 70,000
D. 140,000
E. 210,000
The difference between lengths of each side of the cube is 1inch, so if you calculate the maximum difference between the actual volume and the estimate volume of the cube, you get \(151^{3}-150^{3}=67,950 ≒70,000\), or
\(150^{3}-149^{3}=67,051 ≒70,000\). Therefore, C is the answer.
Answer: C
A certain cube has 150 inches as the length of one side. If the error of the length of one side is within 1 inch, what is the greatest possible difference between the actual volume and the estimated volume of the cube, in cubic inches?
A. 4,000
B. 7,000
C. 70,000
D. 140,000
E. 210,000
The difference between lengths of each side of the cube is 1inch, so if you calculate the maximum difference between the actual volume and the estimate volume of the cube, you get \(151^{3}-150^{3}=67,950 ≒70,000\), or
\(150^{3}-149^{3}=67,051 ≒70,000\). Therefore, C is the answer.
Answer: C
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