Question 1: A net of a rectangular prism shows all six faces. If the length is 8 cm, width is 3 cm, and height is 4 cm, calculate the total surface area. Identify any common mistake students might make.

Answer: 2(8×3 + 8×4 + 3×4) = 2(24 + 32 + 12) = 2×68 = 136 cm²

Question 2: Construct the net of a triangular prism with a base of 5 cm, height of 4 cm, and length of 10 cm. Identify a common error students might encounter when drawing the net.

Answer: Net includes two triangles and three rectangles. Common mistake: misplacing the rectangles or not aligning the triangles correctly.

Question 3: A student draws a net of a cube but forgets to include one face. How will this mistake affect their calculation of surface area?

Answer: Their surface area will be underestimated because one face is missing, leading to an incomplete net.

Question 4: Calculate the surface area of a rectangular prism with dimensions 10 cm by 6 cm by 4 cm. Show all working.

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

Question 5: Identify the mistake in the following net: A net of a rectangular prism with a length of 7 cm, width of 3 cm, and height of 5 cm shows only four faces instead of six. What is the likely error?

Answer: The student likely forgot to include two of the faces or drew only four faces instead of all six.

Question 6: A net shows four rectangles arranged in a row but misses the two end faces. How does this affect the surface area calculation?

Answer: Surface area will be underestimated because two faces are missing from the net, leading to a lower total area.

Question 7: Calculate the surface area of a triangular-based prism with a base of 6 cm, height of 4 cm, and length of 12 cm, using its net. Show calculations.

Answer: Area of two triangular ends: 2 × (½×6×4) = 2×12=24 cm² Area of three rectangles: (6×12)+(4×12)+(12×12) = 72 + 48 + 144 = 264 cm² Total surface area: 24 + 264 = 288 cm²

Question 8: A student claims that folding the net of a prism will always result in a perfect shape. Explain a potential misconception and how to avoid it.

Answer: The misconception is that students assume all nets fold perfectly without overlaps or gaps. To avoid this, students should check the net layout and folding edges carefully.

Question 9: A net has a face missing, but the student calculates surface area assuming all faces are present. What is the consequence?

Answer: Their total surface area will be overestimated, leading to an incorrect answer since one face is absent but still included in calculations.

Question 10: Challenge: Given a net of a cube with one face incorrectly drawn as a different size, identify how this mistake impacts the surface area calculation and how to correct it.

Answer: The surface area will be incorrect because the face dimensions are mismatched. To correct it, measure all faces accurately and recalculate the total surface area based on actual face sizes.