Lesson 18

Surface Area of a Cube

View Student Lesson

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?

Solution

For access, consult one of our IM Certified Partners.

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.

Solution

For access, consult one of our IM Certified Partners.

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?

Solution

For access, consult one of our IM Certified Partners.

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.

Solution

For access, consult one of our IM Certified Partners.

(From Unit 1, Lesson 14.)

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.

Solution

For access, consult one of our IM Certified Partners.

(From Unit 1, Lesson 13.)

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.

Solution

For access, consult one of our IM Certified Partners.

(From Unit 1, Lesson 12.)