# Cylinder

 Definition: Cylinder is a 3-dimensional figure in the shape of a can of coca-cola :) Example: Cylinder   Directions for the interactivity Click and drag sliders r and h to change cylinder size. Click and drag upper sliders to reveal formula and then answer. Click and drag \alpha to see the circumference unwind (thanks ZBM!). This browser does not have a Java Plug-in. Get the latest Java Plug-in here.
Basic formulas for cylinder with radius a and height h:
• Volume of a cylinder: V = h B and
• Surface Area of a cylinder: SA = 2 B + h L
where
• L=2 r \pi is the perimeter (circumference) of the base (top or bottom circles), аnd
• B =r^2 \pi is the area of the base (top or bottom circles).

Examples of volume and surface areas of cylinders

Check the following examples with the interactivity above.

r h Perimeter of circle:

L=2 r \pi

Area of circle:

B = r^2 \pi

Volume of cylinder:

V = h B

Surface area of cylinder:

SA = 2 B + h L

3 \,cm 7 \,cm \begin{array}{} 2 \cdot 3 \,cm \cdot \pi = 6 \pi \,cm \end{array} \begin{array}{} (3 \,cm)^2 \cdot \pi = 9 \pi \,cm^2 \end{array} 7 \,cm \cdot 9 \pi \,cm^2 =63 \pi \,cm^3 \begin{array}{}2 \cdot 9 \pi \,cm^2 + 7 \,cm \cdot 6 \pi \,cm \\= 60 \pi \,cm^2 \end{array}
3 \,cm 7 \,cm \begin{array}{} 2 \cdot 3 \,cm \cdot \pi = 18,8 \,cm \end{array} \begin{array}{} (3 \,cm)^2 \cdot \pi = 28,2 \,cm^2 \end{array} 7 \,cm \cdot 28,2 \,cm^2 = 197,4 \,cm^3 \begin{array}{}2 \cdot 28,2 \,cm^2 + 7 \,cm \cdot 18,8 \,cm \\= 188,1 \,cm^2 \end{array}
7 \,cm 3 \,cm \begin{array}{} 2 \cdot 7 \,cm \cdot \pi = 14 \pi \,cm \end{array} \begin{array}{} (7 \,cm)^2 \cdot \pi = 49 \pi \,cm^2 \end{array} 3 \,cm \cdot 49 \pi \,cm^2 =147 \pi \,cm^3 \begin{array}{}2 \cdot 49 \pi \,cm^2 + 3 \,cm \cdot 14 \pi \,cm \\= 140 \pi \,cm^2 \end{array}
7 \,cm 3 \,cm \begin{array}{} 2 \cdot 7 \,cm \cdot \pi = 44,0 \,cm \end{array} \begin{array}{} (7 \,cm)^2 \cdot \pi = 153,9 \,cm^2 \end{array} 3 \,cm \cdot 153,9 \,cm^2 = 461,8 \,cm^3 \begin{array}{}2 \cdot 153,9 \,cm^2 + 3 \,cm \cdot 44,0 \,cm \\= 439,8 \,cm^2 \end{array}
4,8 \,cm 1,6 \,m \begin{array}{} 2 \cdot 4,8 \times 10^{-2} \,m \cdot \pi\\= 9,6 \pi \times 10^{-2} \,m \\ = 30,16 \times 10^{-2} \,m \end{array} \begin{array}{} (4,8 \times 10^{-2} \,m)^2 \cdot \pi\\= 2,30 \times 10^{-3} \cdot \pi \,m^2 \\ = 7,24 \times 10^{-3} \, m^2 \end{array} \begin{array}{} 1,6 \,m \cdot 7,24 \times 10^{-3} \, m^2 \\ =1,16 \times 10^{-2} \, m^3 \end{array} \begin{array}{}2 \cdot 7,24 \times 10^{-3} \, m^2 \\ \quad + 1,6 \,m \cdot 30,16 \times 10^{-2} \,m \\ = 49,7 \times 10^{-2} \,m^2 \end{array}

Interactivity 2:

 coming soon ...

Related topics and references (not on this site):