Cone

Parameters of a Cone: Radius of the Base ( $r$), Height of the Cone ( $h$) and Slant Height of a Cone ( $l$) Volume of a Cone $= \frac{1}{3} \pi r^2 h$

Curved surface area of a cone $= \pi r l$

Total surface area of a cone = Curved Surface area + Area of the base $= \pi r^2+ \pi r l$

Also note that $l = \sqrt{r^2+h^2}$

Sphere Parameters of a Sphere: Radius of the Sphere ( $r$)

Volume of the sphere $= \frac{4}{3} \pi r ^3$

Surface area of a sphere $= 4 \pi r^2$

Hemisphere Parameters of a Hemisphere: Radius of the Hemisphere ( $r$)

Volume of the hemisphere $= \frac{1}{2} \{\frac{4}{3} \pi r ^3 \} = \frac{2}{3} \pi r^3$

Total surface area of a hemisphere $= \frac{1}{2} \{4 \pi r^2 \} + \pi r^2 = 3 \pi r^2$ Spherical Shell (hollow)

Parameters of a shell: Internal Radius of the Shell  ( $r$) and External Radius of the Shell ( $R$)

Volume of the shell $= \frac{4}{3} \pi (R^3-r^3)$ (this is also the volume of the material used to make the hollow shell)

External Surface are of spherical shell is the same as that of a sphere of radius R $= 4 \pi R^2$ Hemispherical Spherical Shell (hollow)

Parameters of a hemispherical shell: Internal Radius of the Shell ( $r$) and External Radius of the Shell ( $R$)

Volume of the shell $= \frac{2}{3} \pi (R^3-r^3)$ (this is also the volume of the material used to make the hollow shell)

Total surface are of the shell = outside surface area of the shell + Inside surface area of the shell +area of the ring $= \frac{1}{2} (4\pi R^2) + \frac{1}{2} (4\pi r^2) + (\pi R^2 - \pi r^2)$ $= 2 \pi (R^2+r^2) + \pi (R^2-r^2) = 3 \pi R^2 + \pi r^2$ Cylinder

Parameters of a Cylinder: Radius $(r)$ of the base and Height $(h)$ of the Cylinder.

Area of cross section of a cylinder $= \pi r^2$

Perimeter of the cross section $= 2 \pi r$

Volume of the cylinder $= \pi r ^2 h$

Curved surface area $= 2 \pi r h$

Total surface are of a solid cylinder $= 2 \pi r h + 2 \pi r^2 = 2 \pi r (r + h)$ Hollow Cylinder

Parameters of a hollow cylinder: Internal Radius $(r)$, External Radius $(R)$, Height $(h)$

Thickness of the wall of the cylinder $= (R- r)$

Area of the cross section $= \pi R^2 - \pi r^2 = \pi (R^2-r^2)$

Volume of the material use to make the hollow cylinder = External volume – Internal volume $= \pi R^2 h - \pi r^2 h = \pi (R^2-r^2) h$

External curved surface area $= 2 \pi R h$

Internal curved surface area $= 2 \pi r h$

Total surface area = External curved surface area + Internal curved surface area  + 2 (Area of cross section) $= 2 \pi R h + 2 \pi r h + 2 \pi (R^2-r^2)$