To find the surface area of a cylinder, you need to calculate the areas of its two circular bases and its curved surface (the side).
Formula for Surface Area of a Cylinder
The total surface area (TSA) is given by:
Surface Area=2πr2+2πrh\text{Surface Area}=2\pi r^2+2\pi rhSurface Area=2πr2+2πrh
Where:
- rrr is the radius of the circular base,
- hhh is the height of the cylinder,
- 2πr22\pi r^22πr2 is the combined area of the two circular bases,
- 2πrh2\pi rh2πrh is the curved surface area (the rectangle formed when the side is "unwrapped").
This can also be written as:
Surface Area=2πr(r+h)\text{Surface Area}=2\pi r(r+h)Surface Area=2πr(r+h)
Steps to Calculate
- Calculate the area of the two circular bases: 2×π×r22\times \pi \times r^22×π×r2.
- Calculate the curved surface area: 2×π×r×h2\times \pi \times r\times h2×π×r×h.
- Add these two areas together to get the total surface area.
Example
If a cylinder has a radius of 7 cm and a height of 10 cm:
- Area of bases = 2×π×72=98π2\times \pi \times 7^2=98\pi 2×π×72=98π
- Curved surface area = 2×π×7×10=140π2\times \pi \times 7\times 10=140\pi 2×π×7×10=140π
- Total surface area = 98π+140π=238π≈747.7 cm298\pi +140\pi =238\pi \approx 747.7,\text{cm}^298π+140π=238π≈747.7cm2
Use π≈3.14\pi \approx 3.14π≈3.14 or a more precise value depending on your calculator
. This formula and method apply to right circular cylinders.
