Question

Given: The height of the cone is 12 mm.12 mm52°Which is closest to the volume of the cone?O 236 mm386 mmO 1,105 mm2,965 mm

Answer 1

1105 mm^3

Explanation:

We have that the volume of the cone has the following formula:

`V=(1)/(3)\cdot\pi\cdot r^2\cdot h`

We do not know the radius of the cone, but we can calculate it since a right triangle is formed, by means of the tangent function we can calculate the value of the radius, just like this:

`\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ \text{opposite = 12 mm} \\ \text{adjacent = r} \\ \theta=52\text{\degree} \\ \text{replacing and solving for r} \\ \tan 52=(12)/(r) \\ r=(12)/(\tan 12) \\ r=9.38\text{ mm} \end{gathered}`

We replace the value of the radius to calculate the value of the volume:

Therefore the volume is equal to 1105 cubic millimeters