Sure, let's work out the volume of the cone step-by-step.
We are given:
- The radius [tex]\( r = 9 \)[/tex] mm.
- The height [tex]\( h = 12 \)[/tex] mm.
The formula for the volume of a cone is:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
Step 1: Substitute the known values into the formula:
[tex]\[ V = \frac{1}{3} \pi (9 \text{ mm})^2 (12 \text{ mm}) \][/tex]
Step 2: Calculate [tex]\( r^2 \)[/tex]:
[tex]\[ 9 \text{ mm} \times 9 \text{ mm} = 81 \text{ mm}^2 \][/tex]
Step 3: Multiply the result by the height [tex]\( h \)[/tex]:
[tex]\[ 81 \text{ mm}^2 \times 12 \text{ mm} = 972 \text{ mm}^3 \][/tex]
Step 4: Finally, multiply by [tex]\(\frac{1}{3} \pi \)[/tex]:
[tex]\[ V = \frac{1}{3} \pi \times 972 \text{ mm}^3 \][/tex]
So, the volume of the cone is:
[tex]\[ V = 324 \pi \text{ mm}^3 \][/tex]
Thus, the volume of the cone is [tex]\( 324 \pi \)[/tex] cubic millimeters.
