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Question

# From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid.

A

20

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B

16

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C

18

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D

12

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Solution

## The correct options are B 16 C 18 Height of Cylinder = h = AO =2.4 cm Diameter of Cylinder = 1.4 cm ⇒ Radius of Cylinder = Radius of Cone = OB = r =1.42=0.7 cm Using Pythagoras Theorem on △AOB to find Slant Height (I) of cone, we get AB = l = √h2+r2=√(2.4)2+(0.7)2=√5.76+0.49=√6.25=2.5cm Surface Area of remaining Solid = Surface Area of Cylinder Part + Inner surface Area of Hollow Cone =(2.π.r.h+π.r2)+π.r.l=π.r(2h+r+l) = 227×0.7((2×2.4+0.7+2.5) = 2.2(4.8 + 0.7 + 2.5) = 2.2(8) = 17.60 cm2 Total surface area of the remaining solid =18 cm2 = 0.0018 m2

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