Answer:
The radius of the larger cone is equal to 10 ft.
Step-by-step explanation:
For the smaller cone, we have:
radius = r = 8 ft
slant height = l = 12 ft
slant angle = Ф = sine inverse(l/r)
= sine inverse(8/12)
Ф = 42°
Now
For larger cone, with same slant angle,
Slant height = 15 ft
Radius = r =?
r = l sin(Ф)
r = 15*sin(42°)
r = 15*0.669
r = 10 ft
Hence, the radius of a cone with slant height 15 ft and slant angle 42° would be equal to 10 feet.
