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: 

1. Slant height of frustum. 
2. Total surface area of frustum. 
3. Volume of frustum (π = 3.14)

Answer 1

Given: Radii of the frustum: R = 14 cm (Larger base), r = 8 cm (Smaller base)

Height (h) = 8 cm

π = 3.14

1. Slant Height (l):

`l = sqrt(h^2 + (R - r)^2)`

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

= `sqrt(64 + 6^2)`

= `sqrt(64 + 36)`

= `sqrt(100)`

= 10 cm

2. Total surface area (TSA):

TSA = πl(R + r) + πR² + π^r2

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

= [3.14 × 10 × 22] + [3.14 × 196] + [3.14 × 64]

= 690.8 + 615.44 + 200.96

= 1507.2 cm²

3. Volume of the Frustum (V):

V = `1/3 πh (R^2 + Rr + r^2)`

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

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

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

= 3.14 × 8 × 124

= 3.14 × 992

= 3114.88 cm³