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)
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