Question

The total surface area of cone is 1496 mтИЪ and it's base is 14 cm .find its C.S.A and slant height

Answer 1

{ Formulae of Cone : }

Volume of Cone = 1/3πrh

Curved Surface Area of Cone = πrl

Total Surface Area of Cone = πrl(l+r)

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✒ Answer :

✏ Slant Height = 21.49 cm

✏ Curved Surface Area of Cone = 945.56 cm²


✒ Given:

→ Total Surface Area of Cone = 1496 cm²

→ Radius of base of Cone = 14 cm

✏ To Find : Find the Surface Area of Cone

→ Total Surface Area of Cone = πrl(l+r)

→ 1496 cm² = 22/7 × l ( l + 14)

→ 1496 × 7 = 22l(l+14)

→ 10,472 cm² = 22l² + 308

→ 10,472 - 308 = 22 l²

→ 10164 cm² = 22l²

→ 462 = l²

→ l = 21. 49 cm


Now, According to the Questions:

Curved Surface Area of Cone = πrl

→Curved Surface Area of Cone = 22/7 × 14 × 21.49

→Curved Surface Area of Cone = 66l8.92 cm² / 7 cm


→Curved Surface Area of Cone = 945.56 cm²



Hence, Required Value of slant Height and Curved Surface Area of Cone are 21.49 and 945.56 cm² respectively.