Question 1: Calculate the length of the space diagonal of a cuboid with length 8 cm, width 6 cm, and height 4 cm.

Answer: 10

Question 2: Determine the length of the diagonal across the face with length 8 cm and height 4 cm.

Answer: 8.94

Question 3: A cuboid has dimensions 10 cm, 12 cm, and 5 cm. Find the length of its space diagonal.

Answer: 17.46

Question 4: Construct a cuboid on the grid with dimensions 5 cm, 7 cm, and 3 cm. Draw its space diagonal.

Answer: 8.66

Question 5: A storage box is a cuboid measuring 15 cm by 10 cm by 8 cm. Find the length of the diagonal connecting two opposite corners.

Answer: 19.37

Question 6: In a cuboid, the length is 9 cm, width is 4 cm, and the space diagonal is 10 cm. Find the height.

Answer: 6.3

Question 7: A cube has side length 6 cm. Calculate its space diagonal.

Answer: 10.39

Question 8: A rectangular prism measures 10 cm, 4 cm, and 6 cm. Calculate the length of its face diagonal across the 10 cm by 6 cm face.

Answer: 11.66

Question 9: Identify and correct the mistake: A student claims the space diagonal of a cuboid with dimensions 12 cm, 5 cm, and 9 cm is 15 cm.

Answer: Incorrect, the actual diagonal is approximately 15.65 cm.

Question 10: A storage tank in the shape of a cuboid has dimensions of 20 m, 15 m, and 10 m. Find the length of the diagonal from one corner at the bottom to the opposite top corner.

Answer: 27.18

Question 11: Challenge: A cuboid's length, width, and height are all integers. Its space diagonal is 25 cm. If the length is 7 cm, find the possible values for width and height.

Answer: Possible pairs: (24, 16), (15, 20), etc., based on Pythagoras in 3D.