what is the volume of this cone? diameter 22 mm height 19 mm round your answer to the nearest hundredth. use pie = 3.14

1 answer

To calculate the volume of a cone, you can use the formula:

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

where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.

  1. Find the radius: The diameter of the cone is 22 mm, so the radius \( r \) is:

\[ r = \frac{22}{2} = 11 \text{ mm} \]

  1. Use the height: The height \( h \) of the cone is given as 19 mm.

  2. Plug in the values into the volume formula:

\[ V = \frac{1}{3} \times 3.14 \times (11)^2 \times 19 \]

  1. Calculate \( (11)^2 \):

\[ (11)^2 = 121 \]

  1. Now substitute that into the volume formula:

\[ V = \frac{1}{3} \times 3.14 \times 121 \times 19 \]

  1. Calculating \( 121 \times 19 \):

\[ 121 \times 19 = 2299 \]

  1. Now substitute back into the volume formula:

\[ V = \frac{1}{3} \times 3.14 \times 2299 \]

  1. Calculate \( 3.14 \times 2299 \):

\[ 3.14 \times 2299 = 7210.86 \]

  1. Now divide by 3:

\[ V = \frac{7210.86}{3} \approx 2403.62 \]

Thus, the volume of the cone is approximately

\[ \boxed{2403.62 \text{ mm}^3} \]

rounded to the nearest hundredth.