The fraction of a circle represented by the shaded region is:
S '/ S = ((8/5) * pi * r) / (2 * pi * r)
Rewriting we have:
S '/ S = ((8/5)) / (2)
S '/ S = 8/10
S '/ S = 4/5
Then, we can make the following rule of three:
(64/5) pi -------> 4/5
x ----------------> 1
Clearing x we have:
x = ((1) / (4/5)) * ((64/5) pi)
Rewriting:
x = (5/4) * ((64/5) pi)
x = (5/4) * ((64/5) pi)
x = 50.24
Answer:
The area of the complete circle is:
x = 50.24
ANSWER :
Surface area of larger cone : 24π units^2
Surface area of smaller cone : 6π units^2
The surface area of the smaller cone is 25% of that of the larger cone.
EXPLANATION :
From the given problem,
AB = 3 is the radius of the larger cone and the slanted height is BC = 5
DE = 1.5 is the radius of the smaller cone and the slanted height is EC = 2.5
Recall the surface area of the cone :

where r = radius and L = slanted height.
For the larger cone, r = 3 and L = 5

For the smaller cone, r = 1.5 and L = 2.5

Comparing the surface areas :
The area of the smaller cone compared to the larger cone is :
The answer is 48--- 64% of 75=48