Answer:
8 inches
Step-by-step explanation:
The surface area of a cone (without the base) is given by:
Surface area = pi*r*s
Where r is the base radius and s is the slant height.
The smaller cone has a surface area of 41.6pi in2 and a radius of 6.4 inches, so the slant height is:
41.6pi = pi*r*s
41.6 = 6.4s
s = 6.5 in
If the cones are similar, the radius and the slant height increase in the same proportion, so we have that:
r'/s' = r/s = 6.4/6.5
s' = r'*6.5/6.4
So for the larger cone, we have:
65pi = pi*r'*s'
65 = r'*r'*6.5/6.4
r'^2 = 64
r' = 8 inches
