Question 1: Calculate 3³.

Answer: 27

Question 2: What is the cube of 5?

Answer: 125

Question 3: List all perfect cubes from 1³ to 10³.

Answer: 1,8,27,64,125,216,343,512,729,1000

Question 4: Calculate 8³ and verify it equals 512.

Answer: 8³=512

Question 5: A cube has side length 4 units. Find its volume using cube numbers.

Answer: 64

Question 6: If a box's volume is 343 cubic units, what is the length of its side?

Answer: 7

Question 7: Explain why 45 is not a perfect cube, but 27 is.

Answer: 45 is not a perfect cube because it cannot be expressed as n³ for any integer n; 27 is a perfect cube because 3³=27.

Question 8: A cube's side length doubles. How does this affect its volume, in terms of cube numbers?

Answer: The volume increases by a factor of 2³=8; if original volume is n³, new volume is (2n)³=8n³.

Question 9: Construct a cube with a side length of 6 units on the grid. What is its volume in cubic units?

Answer: 216

Question 10: Identify and correct the mistake: A student claims 9³=729, but writes 9²=81.

Answer: The mistake is in the explanation; 9³=729, but 9²=81. The student confuses the two exponents.

Question 11: Calculate the cube of 10 and compare it to 1000. Are they equal?

Answer: 10³=1000, so yes, they are equal.

Question 12: Challenge: Find the smallest perfect cube greater than 500 but less than 1000.

Answer: 729