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प्रश्न
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.
उत्तर
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.
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