Question

A cone is shown. The radius of the base circle is 6 feet. A line is drawn from the center point of the base circle to the apex and has a length of 15 feet.
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

Answer 1

The vertical plane through the axis cuts the cone in an isosceles triangle whose base is the diameter of the base circle (2·6 = 12 ft) and whose height is the cone's height (15 ft).
Area = 1/2 · base · height = 1/2 · 12 · 15 = 90 ft².

Answer: triangle; area = 90 ft².