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A solid metallic right circular cylinder of base diameter 16 cm and height 2 cm is melted and recast into a right circular cone of height three times that of the cylinder. What is the curved surface area (in cm2) of the cone? (Take π = 3.14)

A solid metallic right circular cylinder of base diameter 16 cm and height 2 cm is melted and recast into a right circular cone of height three times that of the cylinder. What is the curved surface area (in cm2) of the cone? (Take π = 3.14) Correct Answer 251.2

Radius of cylinder R = 16/2 = 8 cm

Height of the cylinder H = 2 cm

Height of the cone(h) = 2 × 3 = 6 cm

Let the radius of the cone be r cm.

According to the question

⇒ πr2H = 1/3 × π × r2 × h

⇒ 8 × 8 × 2 = 1/3 × r2 × 6

⇒ r = 8 cm

⇒ l2 = h2 + r2

⇒ l2 = 62 + 82 = 36 + 64 = 100

⇒ l = √100 = 10

⇒ Curved surface area of cone = πrl = 3.14 × 10 × 8 = 251.2

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