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.

Answer 1

The guy above was somewhat right but they made a mistake when finding the volume of the cylinder. The height of the cylinder is 18 mm, not 24mm. 24mm is the height of the cone. The correct answer is 2,016π mm³.

Hope this helps!

Explanation:

Answer 2

For us to easily determine the volume of the figure, let's cut it into two pieces.

Dimension of Cone:

Radius = 9 mm

Height = 24 mm

Dimension of Cylinder:

Radius = 9 mm

Height = 18 mm

For the total volume of the figure, we will be using the following formula:

`\text{ Total volume = Volume of Cone + Volume of Cylinder}`
`\text{ Total volume = }(1)/(3)\pi r^2h\text{ + }\pi r^2h`

We get,

`\text{ Total volume = }(1)/(3)\pi(9)^2(24)\text{ + }\pi(9)^2(24)`
`\text{ = (81)(8)}\pi\text{ + (81)(24)}\pi`
`\text{ = }648\pi\text{ + }1,944\pi`
`\text{ Total volume = }2,592\pi mm^3`

Therefore, the answer is Choice D : 2,592 mm³