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

ANSWER:

1105 mm^3

STEP-BY-STEP EXPLANATION:

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

$V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h$

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:

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

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

$\begin{gathered} V=\frac{1}{3}\cdot3.14\cdot9.38^2\cdot12 \\ V=1105.08\cong1105\operatorname{mm} \end{gathered}$

Therefore the volume is equal to 1105 cubic millimeters