Question 1: What is the net of a rectangular prism with length 8 cm, width 3 cm, and height 5 cm? Draw and label the net.

Answer: A net with 2 rectangles of 8x3, 8x5, and 3x5 arranged appropriately.

Question 2: Calculate the total surface area of a rectangular prism with dimensions 10 cm by 4 cm by 6 cm using its net.

Answer: 2(10×4 + 10×6 + 4×6) = 2(40 + 60 + 24) = 2(124) = 248 cm²

Question 3: Construct a net for a triangular prism with equilateral triangle bases of side 6 cm and length 10 cm.

Answer: Two triangles of 6 cm sides and three rectangles of 6×10 cm arranged accordingly.

Question 4: A cube has an edge length of 5 cm. How many square faces are in its net, and what is the total area?

Answer: 6 faces; total area = 6×(5×5) = 6×25 = 150 cm²

Question 5: Explain how to identify the correct net of a rectangular prism from multiple options.

Answer: Look for the arrangement of rectangles that can fold to form the prism—opposite faces are congruent and properly aligned.

Question 6: A pentagonal prism has a regular pentagon base with a side length of 4 cm and height of 12 cm. Draw its net.

Answer: A net with two pentagons of 4 cm sides and five rectangles of 4×12 arranged accordingly.

Question 7: Calculate the surface area of a triangular prism with triangular bases of side 6 cm and height 4 cm, length 10 cm.

Answer: Area of triangle = (1/2)×6×4=12 cm²; total surface area = 2×12 + (3×6×10) = 24 + 180 = 204 cm²

Question 8: Identify the common mistake students make when calculating the surface area from a net and explain how to avoid it.

Answer: Common mistake: double counting overlapping faces or missing faces. To avoid it, carefully list all faces and verify each is counted once.

Question 9: Design a net for a hexagonal prism with side length 3 cm and height 7 cm.

Answer: A net with two hexagons of 3 cm sides and six rectangles of 3×7 arranged to fold into the prism.

Question 10: A student draws a net that appears to be for a rectangular prism but has three rectangles of different sizes. Identify and correct the mistake.

Answer: The mistake is that opposite faces of a rectangular prism are not congruent. Correct by ensuring pairs of opposite faces are equal in size.