Definitions [5]
A cylinder is a three-dimensional solid figure that has two identical circular bases joined by a curved surface at a particular distance from its centre, which is its height.
The solid obtained on revolving a right-angled triangle about one of its sides (other than the hypotenuse) is called a cone or a right circular cone.
A sphere is a solid obtained by revolving a circle about any one of its diameters.
The radius of the sphere is equal to the radius of the circle revolved.
The solid obtained on revolving a right-angled triangle about one of its sides (other than the hypotenuse) is called a cone or a right circular cone.
A sphere is a solid obtained by revolving a circle about any one of its diameters.
The radius of the sphere is equal to the radius of the circle revolved.
Formulae [6]
Curved surface area of a cylinder = circumference of base × height
= 2πrh
Total surface area = Curved surface area + 2 (Area of cross-section)
= 2πrh + 2πr2
= 2πr(r + h)
Volume = Area of cross-section × height (or, length)
= πr2h
- Volume = \[\frac{1}{3}\pi r^2h\]
-
Curved (lateral) surface area = πrl or \[\pi r\sqrt{h^{2}+r^{2}}\]
(\[l=\sqrt{h^2+r^2}\]) -
Total surface area =
Sphere (radius = r)
-
Volume =\[\frac{4}{3}\pi r^3\]
-
Surface Area = 4πr2
Spherical Shell (external radius R, internal radius r)
-
Thickness = R − r
-
Volume of material = \[\frac{4}{3}\pi(R^3-r^3)\]
- Volume = \[\frac{1}{3}\pi r^2h\]
-
Curved (lateral) surface area = πrl or \[\pi r\sqrt{h^{2}+r^{2}}\]
(\[l=\sqrt{h^2+r^2}\]) -
Total surface area =
Sphere (radius = r)
-
Volume =\[\frac{4}{3}\pi r^3\]
-
Surface Area = 4πr2
Spherical Shell (external radius R, internal radius r)
-
Thickness = R − r
-
Volume of material = \[\frac{4}{3}\pi(R^3-r^3)\]
Cylinder + Two Hemispheres
TSA = CSA of cylinder + 2 × CSA of hemisphere
Cone + Hemisphere
TSA = CSA of cone + CSA of hemisphere
Cube + Hemisphere
TSA = TSA of cube − area of circular base + CSA of hemisphere
