Question

The radii of the circular ends of a frustum of a cone are 14 cm and 8 cm. If the height of the frustum is 8 cm, find: (π = 3.14)

1. Curved surface area of frustum.
2. Total surface area of the frustum.
3. Volume of the frustum.

Answer 1

r₁ = 14 cm, r₂ = 8 cm, h = 8 cm

Slant height of the frustum = l = `sqrt(h^2 + (r_1 - r_2)^2)`

= `sqrt(8^2 + (14 - 8)^2)`

= `sqrt((8)^2 + (6)^2)`

= `sqrt(64 + 36)`

= `sqrt(100)`

= 10 cm

(i) Curved surface area of the frustum = π(r₁ + r₂)l

= 3.14 × (14 + 8) × 10

= 3.14 × 22 × 10

= 3.14 × 220

= 690.8 cm²

(ii) Total surface area of frustum = `πl(r_1 + r_2) + πr_1^2 + πr_2^2`

= 3.14 × 10(14 + 8) + (3.14 × 14)² + (3.14 × 8)²

= 3.14 × 10(22) + (3.14 × 14)² + (3.14 × 8)²

= 3.14 × 220 + (3.14 × 14)² + (3.14 × 8)²

= 690.8 + 3.14 × 14² + 3.14 × 8²

= 690.8 + 3.14 × 196 + 3.14 × 64

= 690.8 + 615.44 + 200.96

= 1507.2 cm²

(iii) Volume of the frustum = `1/3 pih(r_1^2 + r_2^2 + r_1 xx r_2)`

= `1/3 xx 3.14 xx 8 xx (14^2 + 8^2 + 14 xx 8)`

= `1/3 xx 3.14 xx 8 xx (196 + 64 + 112)`

= `1/3 xx 3.14 xx 8 xx (372)`

= `1/3 xx 3.14 xx 2976`

= `1/3 xx 9344.64`

= 3114.88 cm³