Question

Two similar cones are shown in the image below.
What is the approximate surface area of the larger cone?

Answer 1

Because the cones are similar, ratio of corresponding linear parts are in proportion.
The slant height of the larger cone is to the slant height of the smaller cone as the radius of the base of the larger cone is to the radius of the base of the smaller cone.
28/24 = r/8
7/6 = r/8
6r = 56
r = 28/3

The surface area of the larger cone is the sum of its lateral area and its base area.
SA = pi*r*L + pi*r^2 where L is the slant height
SA = pi*(28/3)*28 + pi* (28/3)^2
SA = (3136/9)pi or approx 1094.67 square yards