To calculate the volume of the drill bit, we need to find the volumes of the cone and the cylinder separately and add them together.

Step 1: Volume of the cylinder

The formula for the volume of a cylinder is:

$V_{\text{cylinder}} = \pi r^2 h$

From the diagram:

• Radius $r = 9 \, \text{mm}$,
• Height $h = 18 \, \text{mm}$.

Substitute into the formula:

$V_{\text{cylinder}} = \pi (9)^2 (18) = \pi (81)(18) = 1458\pi \, \text{mm}^3$

Step 2: Volume of the cone

The formula for the volume of a cone is:

$V_{\text{cone}} = \frac{1}{3} \pi r^2 h$

From the diagram:

• Radius $r = 9 \, \text{mm}$,
• Height $h = 24 \, \text{mm}$.

Substitute into the formula:

$V_{\text{cone}} = \frac{1}{3} \pi (9)^2 (24) = \frac{1}{3} \pi (81)(24) = \frac{1}{3} \pi (1944) = 648\pi \, \text{mm}^3$

Step 3: Total volume of the drill bit

Add the two volumes together:

$V_{\text{total}} = V_{\text{cylinder}} + V_{\text{cone}} = 1458\pi + 648\pi = 2106\pi \, \text{mm}^3$

Final Answer:

B. $2106\pi \, \text{mm}^3$

Would you like further clarification on this solution?

Related Questions:

1. How would the volume change if the radius or height were doubled?
2. What is the surface area of the drill bit, including the cone and cylinder?
3. How do you calculate the slant height of the cone in this drill bit?
4. How can the volume of a truncated cone be calculated if the tip is cut off?
5. How does the relationship between radius and height affect the proportions of the cone and cylinder?

Tip: When calculating the volume of composite shapes, always treat each component separately before combining the results.