The measurements obtained for the interior dimensions of a rectangular box are 200 cm by 200 cm by 300cm. If each of the three measurements has an error of at most 1 centimeter, which of the following is the closest maximum possible difference, in cubic centimeters, between the actual capacity of the box and the capacity computed using these measurements?

A. 100,000B. 120,000

C. 160,000

D. 200,000

E. 320,000

Question

Mathematics

Nikolai Ritter

3 February, 22:23

The measurements obtained for the interior dimensions of a rectangular box are 200 cm by 200 cm by 300cm. If each of the three measurements has an error of at most 1 centimeter, which of the following is the closest maximum possible difference, in cubic centimeters, between the actual capacity of the box and the capacity computed using these measurements?

A. 100,000B. 120,000

C. 160,000

D. 200,000

E. 320,000

+3

Answers (2)

Know the Answer?

Brooks Terry · Answer 1

C

Step-by-step explanation:

201*201*301=12160701

199*199*299=11840699

Young · Answer 2

Answer: C. 160,000

Step-by-step explanation:

The measurements obtained for the interior dimensions of a rectangular box are 200 cm by 200 cm by 300cm. If each of the three measurements has an error of at most 1 centimeter, it means that the actual measurement would be

(200 - 1) cm by (200 - 1) cm by (300 - 1) cm. It becomes

199cm by 199 cm by 299 cm

Therefore, the computed capacity would be

200 * 200 * 300 = 12000000 cm^3

The actual capacity would be

199 * 199 * 299 = 11840699 cm^3

The difference, in cubic centimeters, between the actual capacity of the box and the capacity computed would be

12000000 - 11840699 = 159301

Approximately 160000 cm^3