Question 1: Calculate the total surface area of a rectangular prism with length 8 cm, width 5 cm, and height 4 cm. Add all the faces carefully.

Answer: 124

Question 2: A cube has side length 6 cm. An error is made when adding its faces, resulting in a total of 144 cm². Identify and correct the mistake.

Answer: The correct surface area is 216 cm²; mistake was adding only 4 faces instead of 6.

Question 3: Construct a triangular prism with a triangular base of sides 5 cm, 7 cm, and 9 cm, and a height of 10 cm. Show how to find the combined area of the faces you add.

Answer: Sum of two triangular faces (2 × ½ × 5 × 7 + 2 × ½ × 7 × 9 + 2 × ½ × 5 × 9) plus 3 rectangles (10×5 + 10×7 + 10×9) = 161 + 410 = 571 cm²

Question 4: In a rectangular prism, a student mistakenly counts only the vertical faces when calculating total surface area. Explain why this is incorrect and what faces are missing.

Answer: This approach misses the top and bottom faces. The total includes all six faces, not just the vertical ones.

Question 5: Calculate the surface area of a prism with length 12 cm, width 4 cm, and height 3 cm. Show all face additions.

Answer: 2(12×4 + 12×3 + 4×3) = 2(48 + 36 + 12) = 2(96) = 192 cm²

Question 6: A student adds only the lateral faces of a prism and claims this as the total surface area. Explain the mistake and provide the correct total.

Answer: Lateral faces are only part of the surface area. The total must include the base faces as well, so total = lateral area + area of two bases.

Question 7: A rectangular prism has dimensions 10 cm by 7 cm by 3 cm. If a student mistakenly counts only four faces assuming opposite faces are equal, what is the error? Correct the calculation.

Answer: The mistake is counting only four faces instead of all six. Correct total surface area = 2(10×7 + 10×3 + 7×3) = 2(70 + 30 + 21) = 2(121) = 242 cm²

Question 8: Estimate the surface area of a cylindrical prism with radius 4 cm and height 10 cm, focusing only on the curved surface. Then, explain why this is incomplete.

Answer: Curved surface area = 2πrh ≈ 2×3.14×4×10 ≈ 251.2 cm². This omits the areas of the top and bottom circles, so it’s incomplete.

Question 9: Calculate the total surface area of a prism with base area 20 cm² and lateral surface area 60 cm². Show how adding faces is performed.

Answer: Total surface area = lateral area + 2× base area = 60 + 2×20 = 100 cm²

Question 10: A prism's total surface area is calculated as 150 cm². If the student double counts one face, what is the actual surface area? How should they correct their work?

Answer: Double counting face adds extra area. Actual = 150 - area of the double-counted face. To correct, count each face once and sum.

Question 11: A student tries to find the surface area of a prism by adding the areas of three visible faces only. Explain why this is insufficient, and list what other faces must be included.

Answer: This only accounts for some faces. The total includes all six faces — top, bottom, and four sides. Missing faces lead to underestimation.