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. 1,620π mm³ b. 2,592π mm³ c. 2,106π mm³ d. 1,458π mm³
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 volume of drill - bit
The volume of the drill - bit $V = V_{cylinder}+V_{cone}$. Substitute the values of $V_{cylinder}$ and $V_{cone}$: $V=1458\pi + 648\pi=2106\pi$ $mm^{3}$.
Answer:
C. $2,106\pi$ $mm^{3}$