The equation V=1/3πr^2h shows how the volume of a circular cone is related to its height and the radius of its base. When the cone is 3 feet high, the equation becomes V=πr^2. Find the volume of a 3-foot-high circular cone when the radius of its circular base is 2 feet. Round the answer to two decimal places.(1 point)

Question

The volume of the circular cone is __ cubic feet

Answer 1

To find the volume of a circular cone with a height of 3 feet and a radius of 2 feet, we can use the formula for the volume of a cone, which is:

\[ V = \frac{1}{3} \pi r^2 h \]

In this case, the height \( h = 3 \) feet and the radius \( r = 2 \) feet. Plugging these values into the formula, we have:

\[ V = \frac{1}{3} \pi (2)^2 (3) \]

Calculating \( (2)^2 \):

\[ (2)^2 = 4 \]

Now substituting this back into the volume equation:

\[ V = \frac{1}{3} \pi (4) (3) \]

Now, multiply \( 4 \) by \( 3 \):

\[ 4 \times 3 = 12 \]

Now we have:

\[ V = \frac{1}{3} \pi (12) \]

Now divide \( 12 \) by \( 3 \):

\[ \frac{12}{3} = 4 \]

So now we have:

\[ V = 4\pi \]

Finally, substituting the value of \( \pi \approx 3.14159 \):

\[ V \approx 4 \times 3.14159 \approx 12.56636 \]

Rounding this to two decimal places, we get:

\[ V \approx 12.57 \text{ cubic feet} \]

Thus, the volume of the circular cone is approximately 12.57 cubic feet.