Question

identifying cross sections and finding area. what is the type of two - dimensional solid created by a vertical cross section of the cone that passes through the apex? what is the area of the cross section? triangle, area = 45 ft²; triangle, area = 90 ft²; circle, area = 36π ft²; circle, area = 144π ft²

Explanation:

Step1: Identify cross - section shape

A vertical cross - section of a cone passing through the apex is a triangle. The base of the triangle is the diameter of the cone's base and the height is the height of the cone.
The radius of the cone's base $r = 6$ ft, so the diameter $d=12$ ft, and the height of the cone $h = 15$ ft.

Step2: Calculate cross - section area

The area formula for a triangle is $A=\frac{1}{2}\times base\times height$. Here, the base of the triangle is the diameter of the cone's base and the height is the height of the cone.
$A=\frac{1}{2}\times d\times h=\frac{1}{2}\times12\times15 = 90$ $ft^{2}$

Answer:

triangle, area = 90 $ft^{2}$