Read till taught in 8th ConeSolid ConeLet h be the height, l be the slant height and r be the radius of a right circular cone then Curved (lateral) surface area of the solid coneCurved surface area = πr√(r^{2} + h^{2})Total surface area of a solid coneTotal surface area = curved surface area + area of the circular base= πrl + πr^{2} = πr(l+r) Volume of a solid coneVolume= (1/3)πr^{2}h CylinderSolid CylinderLet h be the height and r be the radius of a solid cylinder then Curved surface area of a solid cylinderCurved surface area = perimeter of cross-section × height= 2πrh Total surface area of a solid cylinderTotal surface area = curved surface area + area of two circular ends= 2πrh + 2πr^{2} = 2πr(h+r) Volume of a solid cylinderVolume = area of cross-section × height= πr^{2}×h Hollow CylinderLet r and R be the internal and external radii of the hollow cylinder then Thickness of the cylinder = R − r Area of the cross-section = π(R^{2} − r^{2}) Curved surface area of the hollow cylinderInternal Curved surface area = perimeter of internal cross-section × height= 2πrh External Curved surface area = perimeter of external cross-section × height = 2πRh Total surface area of the hollow cylinderTotal surface area = Internal curved surface area + External curved surface area + area of two ends= 2πrh + 2πRh + 2π(R^{2} − r^{2}) = 2π(rh + Rh + R^{2} − r^{2}) Volume of the hollow cylinderVolume = area of cross-section × height= π(R^{2} − r^{2})×h SphereSolid SphereLet r be the radius of a solid sphere then Surface area of a solid sphereSurface area = 4πr^{2}Volume of the solid sphereVolume = (4/3)πr^{3}HemisphereLet r be the radius of the solid hemisphere then Curved Surface area of a solid hemisphereCurved Surface area = 2πr^{2}Total Surface area of the solid hemisphereTotal Surface area = curved surface area + area of circular base= 2πr^{2} + πr^{2} = 3πr^{2} Volume of the solid hemisphereVolume = (1/2)(4/3)πr^{3} = (2/3)πr^{3}Spherical ShellLet r and R be the inner and outer radii of the spherical shell then Thickness of the shell = R − r Volume of the spherical shellVolume = (4/3)π(R^{3} − r^{3})Hemispherical ShellLet r and R be the inner and outer radii of the spherical shell then Area of base = π(R^{2} − r^{2}) Surface area of the hemispherical shellExternal Curved Surface area = 2πR^{2}Internal Curved Surface area = 2πr^{2} Total Surface area of the hemispherical shellTotal Surface area = 2πR^{2}+ 2πr^{2} + π(R^{2} − r^{2})= π(3R^{2} + r^{2}) Volume of the hemispherical shellVolume of the hemispherical shell = (2/3)π(R^{3} − r^{3}) |
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