Cylinder

A cylinder is similar to a prism except that the cross section of a cylinder is a circle and the sides of a cylinder are curved. A cylinder is not a prism because the sides are not parallelograms.

Here is a cylinder. The radius of the cross section is r and the height of the cylinder is h.

The cross section is a circle like this

Because the cross section is a circle, the area of the cross section is $pi r^2$

The surface area is of the cylinder is made up of two of these circles and the curved area between the circles.

The curved area is a rectangle that has been curved around the circumference of the two circles. The width of the rectangle goes around the circumference of the circle and so it is the same as the circumference of a circe, $2pi r$ . The other dimension is the height of the cylinder. The area of the rectangle is $2pi rh$ .

The surface area of the cylinder is $2pi r^2 + 2pi rh$

The volume of a cylinder is calculated in the same way as the volume of a prism. It is the area of the cross section multiplied by the length. The length of a prism is the same thing as the height of a cylinder. The volume of a cylinder is $pi r^2h$

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Cylinder