Find the radius of a cone if total area = 12 pi and lateral area = 8 pi.

Question

This is a right circular cone and need to find the radius.  The total area = 12 pi and L.A = 8 pi.

Answer 1

Lateral area is πrL=8π where r is the base radius and L the slant length.

Base area=πr².

Total area=lateral area+base area=πrL+πr²=12π.

πr²=total area-lateral area=(12-8)π=4π, therefore r²=4 and r=2.