Volume of water inside the pipe:

$V = \frac{1}{4}\pi(\frac{3}{4})^2(300 \times 12)$

$V = 506.25\pi ~ \text{in.}^3$

$V = 506.25\pi ~ \text{in.}^3 \times \dfrac{1 ~ \text{gallon}}{231 ~ \text{in.}^3}$

$V = 6.885 ~ \text{gallons}$

$V = 6.885 ~ \text{gallons} \times \dfrac{4 ~ \text{quarts}}{1 ~ \text{gallon}}$

$V = 27.54 ~ \text{quarts}$

Therefore, the 10-qt. pail cannot hold all the water in the pipe. The answer is NO.