Given: Total surface area of a cone = 616 sq.cm., slant height of the cone is three times the radius of its base
To find: Slant height (l)
i. Let the radius of base be r cm.
∴ Slant height (l) = 3r cm
Total surface area of cone = πr (l + r)
∴ 616 = πr(l + r)
∴ 616 = \(\sqrt[22]{7}
\) x r x (3r + r)
∴ 616 = \(\sqrt[22]{7}
\) x 4r2
∴ r2 = 49
∴ r = √49 … [Taking square root on both sides]
= 7
ii. Slant height (l) = 3r = 3 x 7 = 21 cm
∴ The slant height of the cone is 21 cm.
