Question

Total surface area of a cone is 616 sq.cm. If the slant height of the cone is three times the radius of its base, find its slant height.

Answer 1

Let the radius of base and slant height of the cone be r cm and l cm, respectively.

Slant height of the cone = 3 × Radius of the cone         ...(Given)

∴ l = 3r

Total surface area of the cone = 616 cm²

∴ πr (r + l) = 616 cm²

⇒ `22/7 xx r xx (r + 3r)` = 616

⇒ `22/7 xx r xx 4r` = 616

⇒ `88/7` r² = 616

⇒ r² = ` [616  xx 7]/88`

⇒ r² = 49

⇒ r = `sqrt 49` = 7cm

∴ Slant height of the cone, l = 3r = 3 × 7 = 21 cm

Thus, the slant height of the cone is 21 cm.