Squares and Cubes

———————————————————————————————————————————————————

Surface Area Review

  • Set the upper slider to L = 1. ​
  • Note the number of squares in the box. ​
  • Move the slider to L = 2 and move the second slider to the right. ​
  • Note the number of squares in the box. ​
  • Continue to repeat the steps until L = 10.

———————————————————————————————————————————————————

Comparing the Area of Different a Rectangle and a Square

  • Use the Ruler or Distance tool to compare the side lengths of the figures.​
  • Use the Angle tool  to verify if the angles are 90 degrees (measure angles in the counter-clockwise direction.)​
  • Use the parallel line tool  to verify that the opposite sides are parallel.

———————————————————————————————————————————————————

To Build a Cube from Unit Cubes.

(A). Use the 32 snap cubes in the applet’s hidden stack to build the largest single cube you can. Each small cube has side length of 1 unit.

(1). How many snap cubes did you use?

(2). What is the side length of the cube you built?

(3). What is the area of each face of the built cube? Show your reasoning in the applet below.

(4). What is the volume of the built cube? Show your reasoning.

(B). The applet below has a total of 64 snap cubes. Build the largest single cube you can.

(1). How many snap cubes did you use?

(2). What is the edge length of the new cube you built?

(3). What is the area of each face of the built cube? Show your reasoning in the applet below.

(4). What is the volume of the built cube? Show your reasoning.

———————————————————————————————————————————————————

Decide if each number on the list is a perfect square.

———————————————————————————————————————————————————

Decide if each number on the list is a perfect cube.

———————————————————————————————————————————————————

Prism A and Prism B are rectangular prisms.

  • Prism A is 3 inches by 2 inches by 1 inch.
  • Prism B is 1 inch by 1 inch by 6 inches.