an engineer is designing a new drill bit as shown in the diagram. to finalize the design, the engineer needs…
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. $2,592pi mm^{3}$ b. $2,106pi mm^{3}$ c. $1,458pi mm^{3}$ d. $1,620pi mm^{3}$
Answer
Explanation:
Step1: Calculate volume of cylinder
The formula for the volume of a cylinder is $V_{cylinder}=\pi r^{2}h$. Given $r = 9$ mm and $h=18$ mm. So $V_{cylinder}=\pi\times9^{2}\times18=\pi\times81\times18 = 1458\pi$ $mm^{3}$.
Step2: Calculate volume of cone
The formula for the volume of a cone is $V_{cone}=\frac{1}{3}\pi r^{2}h$. Given $r = 9$ mm and $h = 24$ mm. So $V_{cone}=\frac{1}{3}\pi\times9^{2}\times24=\pi\times27\times24=648\pi$ $mm^{3}$.
Step3: Calculate total volume
The volume of the drill - bit $V = V_{cylinder}+V_{cone}$. So $V=1458\pi + 648\pi=2106\pi$ $mm^{3}$.
Answer:
B. $2,106\pi$ $mm^{3}$