Question: (a) Given a circular sector with radius L and central angle (see figure), show that the area of the sector is given by S

(a) Given a circular sector with radius L and central angle θ (see figure), show that the area of the sector is given by S = 1/2 L²θ.

(b) By joining the straight-line edges of the sector in part (a), a right circular cone is formed (see figure) and the lateral surface area of the cone is the same as the area of the sector. Show that the area is S = πrL, where r is the radius of the base of the cone.

Figure for 56(a) Figure for 56(b)

(c) Use the result of part (b) to verify that the formula for the lateral surface area of the frustum of a cone with slant height L and radii r₁ and r₂ (see figure) is S = π(r₁ + r₂)L.

Figure for 56(a) Figure for 56(b)

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