Let the radius of the cone be \(r\) cm. ∴ Volume of the cone = \(\frac{1}{3} πr^2 × 12\) cubic cm. According to the condition, \(\frac{1}{3} πr^2 × 12 = 100π\) ⇒ \(4πr^2 = 100π\) ⇒ \(r^2 = 25\) ⇒ \(r = ±5\) ∴ But since the radius of a cone cannot be negative, the radius of the cone = 5 cm ∴ Slant height of the cone \((l) = \sqrt{12^2 + 5^2}\) cm \(= \sqrt{144 + 25}\) cm \(= \sqrt{169}\) cm \(= 13\) cm ∴ The slant height of the cone is 13 cm.