Simplify this paragraph into a few sentences: The formula for the volume of a cone is given by V = (1/3) * π * r^2 * h, where r is the radius and h is the height.
Plugging in the given values, we have V = (1/3) * 3.14 * (4^2) * 12.
Simplifying this expression, we get V = (1/3) * 3.14 * 16 * 12.
Further simplifying, V = (1/3) * 3.14 * 192.
Multiplying the fractions and the decimal, we have V = 0.333 * 3.14 * 192.
Calculating this expression, V ≈ 201.06 cubic feet.
The reason the CORRECT answer is 200.96 and NOT 201.06 is due to rounding. When we round to the nearest hundredth, we look at the digit in the thousandth's place. If this digit is 5 or greater, we round up, and if the digit is less than 5, we round down to the nearest hundredth.
In this case, the digit in the thousandth's place is 6. Since 6 is greater than 5, we round up. However, if we round 201.06 to the nearest hundredth, we would get 201.07, not 201.06 as mentioned in your question.
Therefore, the correct rounded answer to the nearest hundredth is indeed 200.96 cubic feet