Answer: B) 5
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Work Shown:
[tex]V = \frac{4}{3}\pi*r^3\\\\V = \frac{4}{3}\pi*(2t)^3\\\\\frac{4000\pi}{3} = \frac{4}{3}\pi*(2t)^3\\\\4000\pi = 4\pi*(2t)^3\\\\1000 = (2t)^3\\\\(2t)^3 = 1000\\\\(2t)^3 = 10^3\\\\2t = 10\\\\t = 5\\\\[/tex]
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Notes:
- In line 2, I replaced r with 2t because the radius r is increasing at a rate of 2 cm per second. So if t is the number of seconds, then 2t is the radius in cm at time t.
- In line 4, I multiplied both sides by 3 to clear out the fractions. On the next line, I divided both sides by 4pi.
