Lesson 12

Surface Area of a Cube

Let’s write a formula to find the surface area of a cube.

Problem 1

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

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

  3. A cube has a volume of 8 ft3. What is its edge length?

Problem 2

  1. What three-dimensional figure can be assembled from this net?

    six identical squares, net of a cube

  2. 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

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

  2. What is the surface area of this cube?

  3. What is the volume of this cube?

Problem 4

Here is a net for a rectangular prism that was not drawn accurately.

Net of rectangular prism 
  1. Explain what is wrong with the net.
  2. Draw a net that can be assembled into a rectangular prism.
  3. Create another net for the same prism.
(From Unit 1, Lesson 11.)

Problem 5

State whether each figure is a polyhedron. Explain how you know.

Two figures, A and B. Figure A is a cylinder, figure B is a prism with 7 sided polygons as faces.
(From Unit 1, Lesson 11.)

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.

rectangular prism with student's work to calculate surface area shown

She concluded that the surface area of the prism is 296 square feet. Do you agree with her? Explain your reasoning.

(From Unit 1, Lesson 10.)