CEMC Pascal, 2021

Algebra Difficulty 1.7 Junior Find the answer Canada

Three cubes have edge lengths $3$ cm, $12$ cm, and $x$ cm. The average volume of the three cubes is $\text{700 cm 3}$ . The value of $x$ , rounded to the nearest integer, is

Pick one

Solution

Since the average volume of three cubes is $\text{700 cm 3}$ , their total volume is $\text{3 700 cm 3}$ or $\text{2100 cm 3}$ .

The volume of a cube with edge length $s$ cm is $\text{s 3 cm 3}$ .

Therefore, $3^3 + 12^3 + x^3 = 2100$ and so $27 + 1728 + x^3 = 2100$ or $x^3 = 345$ .

Since $x^3 = 345$ , then $x \approx 7.01$ , which is closest to 7.

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