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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 as that of cylinder is hollowed out. Find the total surface area of the remaining solid. (Use π=227)


A

19.60 cm2

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B

18.60 cm2

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C

17.60 cm2

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D

15.60 cm2

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Solution

The correct option is C

17.60 cm2




Height of Cylinder =h=AO=2.4 cm

Diameter of Cylinder =1.4 cm

Radius of Cone = Radius of Cylinder
OB=r=1.42=0.7 cm


Lets find Slant Height l of cone, using pythagoras theorem on AOB , we get

AB=l=h2+r2=(2.4)2+(0.7)2

l=5.76+0.49=6.25=2.5 cm


Surface Area of remaining Solid
= Surface Area of the Cylinder + Inner surface Area of the hollow Cone
=(2πrh+πr2)+πrl=πr(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 is 17.60 cm2


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