Question

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?
o triangle, area = 45 ft²
o triangle, area = 90 ft²
o circle, area = 36π ft²
o circle, area = 144π ft²

Explanation:

Step1: Determine the shape of the cross - section

A vertical cross - section of a cone that passes through the apex is a triangle. The base of the triangle is the diameter of the base of the cone, and the height of the triangle is the height of the cone.
Given the radius \(r = 6\) ft, the diameter \(d=2r = 12\) ft (base of the triangle), and the height \(h = 15\) ft (height of the triangle).

Step2: Calculate the area of the triangle

The area formula for a triangle is \(A=\frac{1}{2}\times base\times height\).
Substitute \(base = 12\) ft and \(height = 15\) ft into the formula:
\(A=\frac{1}{2}\times12\times15\)
\(A = 6\times15\)
\(A=90\) \(ft^{2}\)

Answer:

triangle, area = \(90\) \(ft^{2}\)