Yuri O. answered • 02/13/21

16 years online, 464 former SAT problems drilled down

If we make a cross section of these solids with front plane perpendicular to the ground, we will get a triangle, inscribed into the circle. The triangle is associated with the cone and the circle is associated with the sphere. Vertices of the triangle A, B and C will lie on the circle.

The triangle is equilateral since AB = BC = AC, where AC is the diameter of the cone.

Angles A, B and C have the same measure of 60°.

We will find the length of AB by this formula (Sine Rule):

AB/sin(60°) = 2R_{circle}

**AB** = 2 • 12 • sin(60°) ≅ **20.7846**

**R**_{cone} = (1/2)AB ≅ **10.7846**

BE is the altitude of the cone (point "E" is located half-way between vertices "A" and "C").

ΔABE is the right triangle.

From ΔABE:

**BE** = AB • sin(60°) = 20.7846 • sin(60°) ≅ **18** (ft)

Maddie U.

Thank you!02/13/21