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From a solid cylinder of height h cm and base radius r cm, a conical cavity of the same height and same radius is drilled out.

If the slant height of the conical cavity is l cm, the surface area of the remaining solid is :

  1. 2πrh + πrl

  2. 2πrh - πr2 + πrl

  3. 2πrh + πrl + πr2

  4. 2πrh - πrl + πr2

Mensuration

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Answer

Given,

Radius of cylinder = r cm

Height of cylinder = h cm

Radius of cone = r cm

Height of cone = h cm

From a solid cylinder of height h cm and base radius r cm, a conical cavity of the same height and same radius is drilled out. If the slant height of the conical cavity is l cm, the surface area of the remaining solid is. 1. 2πrh + πrl 2. 2πrh - πr2 + πrl 3. 2πrh + πrl + πr2 4. 2πrh - πrl + πr2. Model Paper 2, Concise Mathematics Solutions ICSE Class 10.

Surface area of remaining solid = Total surface area of cylinder - Base area of cone + Curved surface area of cone

= (2πrh + 2πr2) - (πr2) + πrl

= 2πrh + 2πr2 - πr2 + πrl

= 2πrh + πr2 + πrl

Hence, Option 3 is the correct option.

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