Answer: 60pi cm^2 = 188.5 cm^2
Step-by-step explanation:
You don't need to understand how or why the curved surface area of a cone is pi×r×L. You just need to see that the answer is area big cone minus area small cone.
big cone curved surface area
B = pi × 8 × 10 cm^2 = 80pi cm^2
small cone dimensions. It's similar to big cone so all dimensions scale by same factor, namely 1/2 ("the height of the small cone is half the height of the large cone.")
small cone curved surface area
S = pi × 8/2 × 10/2 cm^2 = 20pi cm^2
Frustum curved surface area = B - S = 60pi cm^2 = 188.5 cm^2
But if you want to know why the curved surface area is pi r L, take a paper cone with base radius r and slant length L, and cut straight from base to apex. It flattens out to the sector of a circle with radius L and arc length 2pi r.
Now the arc length of a full circle of radius L is 2pi L, and its area is pi L^2. So the area is half arc length (pi L) times radius (L).
Arc length of sector is 2pi r
Half arc length is pi r
Radius is L
Area of sector of circle unrolled from cone is pi r L.
