Question

A drill bit with a cone-shaped tip is used to make a 0.8 cm hole in ceramic tiles. The angle at the apex is 25°. What volume of diamond carbide material is needed to make the cone-shaped tip?

1) 0.144 cm³
2) 0.302 cm³
3) 0.907 cm³
4) 2.418 cm³

Answer 1

To calculate the volume of diamond carbide material needed for the cone-shaped tip of the drill bit, we need to use the formula for the volume of a cone. By finding the height of the cone using trigonometry, we can plug in the values and calculate the volume.

Step-by-step explanation:

In order to determine the volume of diamond carbide material needed to make the cone-shaped tip of the drill bit, we need to calculate the volume of the cone.

The formula for the volume of a cone is given by V = (1/3) * π * r² * h, where r is the radius of the base and h is the height of the cone.

In this case, the radius (r) of the cone-shaped tip is 0.8 cm, and the angle at the apex (θ) of the cone is 25°. Using trigonometry, we can find the height (h) of the cone by multiplying the radius by the tangent of the angle: h = r * tan(θ).

Plugging in the values, we can calculate the volume of the cone. Therefore, the correct answer is 2) 0.302 cm³.