# From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid.

Height of solid cylinder = h = 2.8 cm

Diameter of solid cylinder = 4.2 cm

Radius of solid cylinder = r = Diameter ÷ 2 = 2.1 cm

Curved Surface area of solid cylinder = 2πrh

= 2 × 22/7 × 2.1 × 2.8 cm2

= 2 × 22/7 × 2.1 × 2.8 cm2

= 36.96 cm2

Height of conical cavity = h = 2.8 cm

Radius conical cavity = r = 2.1 cm

Let l be the slant height of conical cavity

l2 = r2 + h2

l2 = (2.82 + 2.12) cm2

l2 = (7.84 + 4.41) cm2

l2 = 12.25 cm2

l = 3.5 cm

Curved Surface area of conical cavity = πrl

= 22/7 × 2.1 × 3.5

= 23.1 cm2

Total surface area of remaining solid = Curved surface area of solid cylinder + Curved surface area of conical cavity + Area of circular base

Total surface area of remaining solid = (36.96 + 23.1 + 22/7 × 2.12) cm2

= (36.96 + 23.1 + 13.86) cm2

= 73.92 cm2

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