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Parth had the cylindrical iron piece. He drilled out a conical cavity from the iron piece. The height and radius of the conical cavity is 15 cm and 8 cm respectively which is equal to the eight and radius of cylindrical iron piece. Find the total surface area of the remaining cylindrical iron piece.

Parth had the cylindrical iron piece. He drilled out a conical cavity from the iron piece. The height and radius of the conical cavity is 15 cm and 8 cm respectively which is equal to the eight and radius of cylindrical iron piece. Find the total surface area of the remaining cylindrical iron piece. Correct Answer 440π cm<sup>2 </sup>

Given:

Height and radius of cylinder and cone is 15 cm and 8 cm respectively

Formula used:

Area of circle = πr2

Area of cone = πrl

Area of cylinder = 2πrh

Calculation:

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From figure

(Slant height of cone)2 = (Radius of cone)2 + (height of cone)2

⇒ (l)2 = 82 + 152

⇒ l = √(64 + 225) = √289 = 17 cm

Total surface area of remaining portion = base area of one side of iron piece + curved surface area of conical cavity + curved surface area of the cylindrical piece

⇒ T.S.A = πr2 + π rl + 2πrh

⇒ T.S.A = π × (8)2 + π × 8 × 17 + 2 × π × 8 × 15

⇒ T.S.A = π × 8 × (8 + 17 + 30) = π × 8 × 55 = 440π cm2

∴ Total surface area of remaining cylindrical iron piece = 440π cm2

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