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
| 2 \cdot 9 \pi \,cm^2 + 7 \,cm \cdot 6 \pi \,cm = 60 \pi \,cm^2
|
| 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
| 2 \cdot 28,2 \,cm^2 + 7 \,cm \cdot 18,8 \,cm = 188,1 \,cm^2
|
| 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
| 2 \cdot 49 \pi \,cm^2 + 3 \,cm \cdot 14 \pi \,cm = 140 \pi \,cm^2
|
| 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
| 2 \cdot 153,9 \,cm^2 + 3 \,cm \cdot 44,0 \,cm = 439,8 \,cm^2
|
| 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}
|
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