From a solid cylinder whose height is 12 cm and diameter 10 cm a conical cavity of the same height and same diameter is hollowed out. Find the volume and total surface area of the remaining solid
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Volume of remaining solid = Volume of cylinder - Volume of Cone
In the given case,
r = 5cm
h = 12cm
Volume of Cylinder = pi * r * r * h = 3.14 * 5 * 5 * 12 = 942 cm^3
Volume of Cone = (1/3) * pi * r * r * h = (1/3) * 3.14 * 5 * 5 * 12 = 314 cm^3
Remaining Volume = 942 - 314 = 628cm^3
Total Surface of Remaining Solid = Conical surface area of Cone + Area of Circle + Cylindrical area of Cylinder
Conical surface area of Cone = pi * r * ((r^2 + h^2)^(1/2)) = 282.74cm^2
Area of Circle = pi * r * r = 78.54cm^2
Cylindrical area of Cylinder = 2 * pi * r * h = 376.8cm^2
Total Surface Area = 738.08cm^2
In the given case,
r = 5cm
h = 12cm
Volume of Cylinder = pi * r * r * h = 3.14 * 5 * 5 * 12 = 942 cm^3
Volume of Cone = (1/3) * pi * r * r * h = (1/3) * 3.14 * 5 * 5 * 12 = 314 cm^3
Remaining Volume = 942 - 314 = 628cm^3
Total Surface of Remaining Solid = Conical surface area of Cone + Area of Circle + Cylindrical area of Cylinder
Conical surface area of Cone = pi * r * ((r^2 + h^2)^(1/2)) = 282.74cm^2
Area of Circle = pi * r * r = 78.54cm^2
Cylindrical area of Cylinder = 2 * pi * r * h = 376.8cm^2
Total Surface Area = 738.08cm^2
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