an engineer is designing a new drill bit as shown in the diagram. to finalize the design, the engineer needs…

Answer:

C. $1,620\pi\ \text{mm}^3$

Explanation:

Step1: Calculate cylinder volume

The formula for the volume of a cylinder is $V_{cylinder}=\pi r^{2}h$. Given $r = 9\ \text{mm}$ and $h=18\ \text{mm}$, so $V_{cylinder}=\pi\times9^{2}\times18=\pi\times81\times18 = 1458\pi\ \text{mm}^3$.

Step2: Calculate cone volume

The formula for the volume of a cone is $V_{cone}=\frac{1}{3}\pi r^{2}h$. Given $r = 9\ \text{mm}$ and $h = 24\ \text{mm}$, so $V_{cone}=\frac{1}{3}\pi\times9^{2}\times24=\pi\times27\times24=648\pi\ \text{mm}^3$.

Step3: Calculate total volume

The volume of the drill - bit $V = V_{cylinder}+V_{cone}$. So $V=1458\pi + 162\pi=1620\pi\ \text{mm}^3$.