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.

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) 

Solution:

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

∴  r^{2 = \(\frac{616\,\times\,7}{22 \,\times\,4}\)}

 ^{= \(\frac{28\,\times\,7}{4}\)}

∴ r² = 49 

∴ r = \(\sqrt{49}\)… [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.