Lesson 12: Practice Problems

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 cm?

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

Problem 2

A net made up of 4 squares and 2 more attached at the second square

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

  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 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.

A net made up of 2 sets of equivalent alternating rectangles with a square attached below the last rectangle and another square attached above the second rectangle.

  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.

Problem 5

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

  1. cylinder
  2. heptagonal prism

Problem 6 From Unit 1 Lesson 10

Here is Elena’s work for finding the surface area of a rectangular prism that is 1 foot by 1 foot by 2 feet.

A drawing of a rectangular prism that is 1 ft by 1 ft by 2 ft with areas of sides and descriptions of calculations shown.

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