Lesson 12
Surface Area of a Cube
Let’s write a formula to find the surface area of a cube.
Problem 1

What is the volume of a cube with edge length 8 in?

What is the volume of a cube with edge length \(\frac 13\) cm?

A cube has a volume of 8 ft^{3}. What is its edge length?
Problem 2

What threedimensional figure can be assembled from this net?

If each square has a side length of 61 cm, write an expression for the surface area and another for the volume of the figure.
Problem 3

Draw a net for a cube with edge length \(x\) cm.

What is the surface area of this cube?

What is the volume of this cube?
Problem 4
Here is a net for a rectangular prism that was not drawn accurately.
 Explain what is wrong with the net.
 Draw a net that can be assembled into a rectangular prism.
 Create another net for the same prism.
Problem 5
State whether each figure is a polyhedron. Explain how you know.
Problem 6
Here is Elena’s work for finding the surface area of a rectangular prism that is 1 foot by 1 foot by 2 feet.
She concluded that the surface area of the prism is 296 square feet. Do you agree with her? Explain your reasoning.