Geometry: Understanding Cubes

What is a Cube?

• A cube is a 3-dimensional geometric solid with 6 faces, each shaped like a square.
• Each face of a cube is congruent, or identical in size and shape.
• Examples of cubes include sugar cubes, dice, and children's alphabet blocks.

Surface Area of a Cube

• Surface area is the number of unit squares needed to cover the outside surfaces of the solid.
• The surface area of a cube is the sum of the areas of its six faces.
• The formula to calculate the surface area of a cube is: SA = 6s^2, where SA is the surface area and s is the length of one side.

Examples of Surface Area Calculation

• Example 1: Find the surface area of a child's cube-shaped block with a side length of 3 cm. Answer: 54 square cm.
• Example 2: Find the surface area of a sugar cube with a side length of 10 mm. Answer: 600 square mm.
• Example 3: Find the surface area of a cube-shaped gift box with a side length of 4 inches. Answer: 96 square inches.

Finding the Length of One Side of a Cube

• The same formula (SA = 6s^2) can be used to find the length of one side of a cube if given the surface area.
• Example 1: Find the length of one side of a cube with a surface area of 24 square inches. Answer: 2 inches.
• Example 2: Find the length of one side of a cube with a surface area of 216 square cm. Answer: 6 cm.
• Example 3: Find the length of one side of a cube with a surface area of 150 square inches. Answer: 5 inches.

Volume of a Cube

• The volume of a cube measures the amount of space inside the cube.
• The formula to calculate the volume of a cube is: V = s^3, where V is the volume and s is the length of one side.
• Example: Find the volume of a single cube-shaped die with a side length of 8 mm. Answer: 512 cubic mm.