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# Surface Area and Volume of a Cylinder

In geometry, a cylinder is a three-dimensional shape with a circular base, a circular top, and straight sides. It is the solid figure that you get when you rotate a rectangle about one of its sides.

To compute the volume and surface area of a cylinder, you only need to know its height and the radius of its base. The cylinder calculator below will tell you the surface area and volume if you input the height and radius, or you can use the formulas described below.

### Cylinder Volume Formula

For a cylinder with a radius of**R**and a height of

**H**the formula for its volume is

Volume = (pi)R

^{2}H,

where pi is the geometrical constant 3.14159265358...

Example: Suppose a can is 11 cm tall and the diameter of the base is 8 cm. Then we have

**R**= 4 and

**H**= 11. Its volume is

(3.14159)(4

^{2})(11) = 552.92 cm

^{3}or 552.92 mL.

### Cylindrical Surface Area Formula

For a cylinder with a radius of**R**and a height of

**H**, the formula for its total surface area (including both bases) is

Surface Area = 2(pi)RH + 2(pi)R

^{2}.

The surface area formula

*excluding*the top and bottom is simply

Surface Area = 2(pi)RH.

Example: Suppose a can is 10 inches tall, 18 inches wide, and has a label around the outside. To find the area of the label, we use the second surface area formula with

**R**= 9 and

**H**= 10. 2(3.14159)(9)(10) = 565.487 square inches.

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