Question

Find the volume of the right cone. Round your answer to the nearest hundredth.

Answer 1

Answer:

574.82 cubic yards

Step-by-step explanation:

The diameter of the cone =14 yards

The angle between the height and slant height measures 32 degrees.

First, we determine the height of the cone using trigonometry.

In Right Triangle AOB,

$Tan 32=\dfrac{7}{|AO|} \\|AO|*Tan 32 =7\\ Height of the Cone, |AO|=\dfrac{7}{Tan 32} =11.2023 \:yards$

$\text{Volume of a Cone=}\dfrac{1}{3}\pi r^2h\\Volume =\dfrac{1}{3}\pi*7^2*11.2023\\=574.82 cubic yards$

The volume is about  575 cubic yards.