7) A container is shaped like a cone and contains oil. The radius is 7 feet and the height is 8 feet. If the container can release oil from its bottom at the rate of 12 cubic feet per minute, how long would it take for the container to empty fully? Use ( \( \pi=3.14 \) ).

1. The formula for the volume of a cone is given by \[ V=\frac{1}{3}\pi r^2h \] 2. Substitute the given values \( r=7 \) feet and \( h=8 \) feet into the formula: \[ V=\frac{1}{3}\times 3.14 \times 7^2 \times 8 \] 3. Calculate \( 7^2 \): \[ 7^2=49 \] 4. Multiply inside the formula: \[ 3.14 \times 49 \times 8=3.14 \times 392=1230.88 \] 5. Now divide by 3: \[ V=\frac{1230.88}{3}\approx410.2933 \text{ cubic feet} \] 6. The oil is released at a rate of 12 cubic feet per minute, so the time \( t \) (in minutes) to empty the container is: \[ t=\frac{\text{Volume}}{\text{Rate}}=\frac{410.2933}{12}\approx34.1911 \text{ minutes} \] 7. Rounding to one decimal place, it would take approximately \[ t\approx34.2 \text{ minutes} \] for the container to empty fully.