Surface Area of Prisms and Cylinders (10-4)

Surface Area of Prisms and Cylinders

Vocabulary

Net- the flat pattern of a three-dimensional figure.

Surface Area- the sum of the areas of all of the surfaces of a figure expressed in square units.

Lateral Face- parallelograms of a prism that connect the bases.

Lateral Area- the sum of prisms areas of lateral faces.

Examples

How to find the surface area and volume of prisms.

Theory:

A 'prism' is a solid figure with a uniform cross section. Here are some examples of prisms:

Rectangular based prism:

Circular based prism: (Cylinder)

Triangular based prism:

The surface area of any prism equals the sum of the areas of its faces, which include the floor, roof and walls. Because the floor and the roof of a prism have the same shape, the surface area can always be found as follows:
From now on we will call the 'floor' the 'base'. The height of the prism = 'H'.

The surface area of a prism = 2 × area of base  +  perimeter of base × H

The actual formula used to find the surface area will depend on the shape of the base of the prism.
For example:

Rectangular based prism Base shape: Rectangle, length 'L' and width 'W' Area of base: L  × W Perimeter of base: 2(L+W) Surface area = 2LW + 2(L+W)H
Circular based prism Base shape: Circle, radius 'R' Area of base: pR² Perimeter of base: 2pR Surface area = 2pR² + 2pRH
Triangular based prism Base shape: Triangle: base 'b', height 'h', and sides S1, S2 and S3  Area of base: ½b×h Perimeter of base: S1+ S2 + S3 Surface area = bh + (S1+ S2 + S3)H

http://www.teacherschoice.com.au/maths_library/area%20and%20sa/area_9.htm

Video Help

https://www.youtube.com/watch?v=a7EzdWoc1js

https://vimeo.com/124259324

https://www.youtube.com/watch?v=t7h3b16OEHU