Total surface area of a cone is 616 sq.cm. If the slant ‘height of t

1.	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» 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.

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»

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.