Question 1: A cube has all edges of equal length. The surface area of a cube with edge length 5cm is calculated using the formula 6 × (edge length)^2. The volume is given by (edge length)^3. Confirm these formulas are correct and explain why they are suitable for a cube.

Answer: Yes, because a cube has 6 faces each a square with side length, so surface area = 6 × side^2. The volume is the cube of the side length as the space enclosed by the cube is length × width × height, all equal.

Question 1: Calculate the surface area of a cube with edge length 8 cm.

Answer: 384 cm^2

Question 2: Find the volume of a cube with edge length 3.5 meters.

Answer: 42.875 m^3

Question 3: If the surface area of a cube is 150 square centimeters, what is the length of each edge?

Answer: ≈ 5 cm

Question 1: A cube's surface area is doubled from 96 cm^2 to 192 cm^2. What is the new edge length? Show your calculations.

Answer: Edge length increases from 4cm to 8cm because surface area = 6 × side^2. Original side = 4cm, new side = 8cm.

Question 2: A cube with edge length 4 cm is painted on all sides. If a section of the cube is cut out to form a smaller cube with edge length 2 cm, what is the volume of the remaining painted material? Explain your reasoning.

Answer: Original volume = 64 cm^3. Removed cube volume = 8 cm^3. Remaining volume = 56 cm^3.

Question 1: A box in a warehouse is in the shape of a cube with an edge length of 2 meters. How much space does it occupy? If a worker needs to fill the box with small cubes of 0.25 meters edge length, how many small cubes are needed? Show your working.

Answer: Volume of box = 8 m^3. Volume of small cube = 0.015625 m^3. Number needed = 512.

Question 1: A cube is made from a material with density 2.5 g/cm^3. If the cube has an edge length of 12 cm, what is the mass of the cube? Show all steps.

Answer: Mass = volume × density = (12^3) × 2.5 = 1728 × 2.5 = 4320 g.

Question 2: Design a cube with a volume of 125 cm^3. If the side length is decreased by 20%, what is the new volume? Explain your process.

Answer: Original side = 5cm. New side = 4cm. New volume = 4^3 = 64 cm^3.

Question 1: A student calculates the surface area of a cube as 24 cm^2 for an edge length of 2 cm. Identify and correct the mistake in their calculation.

Answer: Incorrect because surface area = 6 × 2^2 = 24 cm^2, which is correct; but perhaps they forgot to multiply by 6 or squared correctly. The calculation is actually correct, so no mistake. Alternatively, if they said 12 cm^2, then the mistake is forgetting to multiply by 6.

Question 2: A student claims the volume of a cube with edge length 4 cm is 64 cm^3. Is this correct? If not, what is the correct volume?

Answer: Yes, because 4^3 = 64 cm^3.