How to Find the Surface Area and Volume of a Cube

Finding the surface area and the volume of different three dimensional shapes can be very useful in the real world. If you want to know how much siding you are going to need for the outside of your house then you are going to want to be able to find the surface area of your house. If you want to know how many balloons you will need to fill a room for a surprise party then you will want to be able to find out the volume of the room as well as the volume of the balloons.

Things You'll Need

• Paper
• Pencil
• Calculator (optional)

Instructions

Finding the Surface Area of a Cube

1. Measure along one edge of the cube.

   A cube is a three dimensional shape that has the same height, depth, and width, so you only need to measure one edge because all the edges have the same measurement.

2. Learn that the surface area of a cube can be expressed by the equation S=6(x^2), where S is the surface area and x is the length of any edge.

   Because the area of one of the square sides is the length of the edge multiplied by the length of the edge we can simplify that by squaring the length of the edge. We then multiply that number by the number of sides of the cube, six.

3. Plug in the length of the edge for x and solve for S.

   If we had a cube that had an edge length of 2 inches then we would find the surface area of that cube like this:

   6(2^2)=S

   6*4=S

   S=24

4. Put your answer in terms of units squared.

   For the cube with the 2 inch edge the surface area would be 24 inches squared.

Finding the Volume of a Cube

1. Use the same edge measurement that you used to find the surface area of the cube to now find its volume.

2. Know that the volume of a cube can be expressed by the equation V=x^3 where V stands for volume and x stands for the length of any edge of the cube.

   The volume of a cube is found by multiplying height*width*depth, and since all of these measurements are the same for a cube this can be simplified into x^3.

3. Plug in the length of any of the cube's edges for x and solve for V.

   For the cube that we were working with earlier with the 2 inch edge we would find its volume by doing the following:

   2^3=V

   16=V

4. Put your answer in terms of units cubed.

   So, for our cube the volume would be 16 inches cubed.

Tips & Warnings

• Always remember to attach units to your answer in the end.