Question

Frustum Question work out the bottom bit of the cone.

Answer 1

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.