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.?

Option 3 : 440π cm2 

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