Question

an engineer is designing a new drill bit as shown in the diagram. to finalize the design, the engineer needs to know the volume of the drill bit. what is the volume of the drill bit? a. 1,458π mm³ b. 2,106π mm³ c. 2,592π mm³ d. 1,620π mm³

Explanation:

Step1: Recall volume formulas

The drill - bit is composed of a cylinder and a cone. The volume formula for a cylinder is $V_{cylinder}=\pi r^{2}h$ and for a cone is $V_{cone}=\frac{1}{3}\pi r^{2}h$. Given $r = 9$ mm, $h_{cylinder}=18$ mm, and $h_{cone}=24$ mm.

Step2: Calculate volume of cylinder

$V_{cylinder}=\pi\times(9)^{2}\times18=\pi\times81\times18 = 1458\pi$ $mm^{3}$.

Step3: Calculate volume of cone

$V_{cone}=\frac{1}{3}\pi\times(9)^{2}\times24=\frac{1}{3}\pi\times81\times24=\pi\times81\times8 = 648\pi$ $mm^{3}$.

Step4: Calculate total volume

$V = V_{cylinder}+V_{cone}=1458\pi+648\pi=2106\pi$ $mm^{3}$.

Answer:

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