The surface area of an object is the total amount of space on the uppermost layer. The volume of an object is the amount of space that said object occupies. This week we learned several things, but one of the, was how to find the surface area, and the volume, or prism and cylinders.

The surface area of a prism, or a cylinder…

*A prism is a three dimensional object that has two bases that are the same size and shape, and are parallel to each other, and each of whose sides is a parallelogram.*

*We study right prisms in this course, which are prisms who’s sides are rectangles, but whose base could be a variety of shapes.*

*A right cylinder also has bases that are parallel, congruent, and aligned. *

The way you caclulate the surface area of a prism is to add all faces of the prisms. There are different formulas used to calculate different shapes. For a circle different formulas are used for different things such as ….

and for a rectangle or a square formulas such as these are used to find the area…

there are other formulas for other shapes as well, such as a triangle…

a parallelogram…

 

and a trapezoid…

Here are some examples of calculating the surface area of right prisms…

…

Calculating the volume of a prism or cylinder uses a similar but different process as calculating the surface area. To calculate the volume of a prism or a cylinder you basically take the area of the base and multiple it by the height, however there are some differences in the formulas depending on the shape.

The volume of a prism is…

The volume of a cylinder is…

Some examples of this process being used are…