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: R = 14 cm (Larger base), r = 8 cm (Smaller base).

Height: h = 8 cm.

Use frustum formulas slant height `l = sqrt(h^2 + (R - r)^2)`; curved surface area = `πl(R + r)`; total surface area = `πl(R + r) + πR^2 + πr^2`; volume = `1/3 πh(R^2 + Rr + r^2)`.

Step-wise calculation:

a. Slant height `l`:

R – r = 14 – 8

= 6 cm

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

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

= `sqrt(64 + 36)`

= `sqrt(100)`

= 10 cm

b. Total surface area (use π = 3.14):

Curved (lateral) area = π × l × (R + r)

= 3.14 × 10 × (14 + 8)

= 3.14 × 10 × 22

= 220 × π 

= 220 × 3.14

= 690.8 cm²

Areas of bases = πR² + πr²

= 3.14 × (14² + 8²) 

= 3.14 × (196 + 64)

= 3.14 × 260

= 816.4 cm²

Total surface area = 690.8 + 816.4

= 1507.2 cm²

Or symbolically: Total = 480π

= 480 × 3.14 

= 1507.2 cm²

c. Volume (use π = 3.14):

R² + Rr + r² = 14² + 14 × 8 + 8² 

= 196 + 112 + 64

= 372

Volume = `1/3 πh (R^2 + Rr + r^2)`

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

Simplify: `8/3 xx 372 xx 3.14`

= 992 × 3.14

= 3114.88 cm³