If the cube has surface area 294 square inches, each face has area 294 ÷ 6 = 49 square inches. When you remove one face from the net, you have 294 - 49 = 245 square inches remaining. Choice A and B both give the correct numerical answer, but A provides the more direct reasoning. Choice C incorrectly gives just the area of the removed face rather than what remains. Choice D incorrectly suggests the net requires extra material beyond the surface area.

The correct prism has dimensions 9×4×6, giving surface area 2(9×4) + 2(9×6) + 2(4×6) = 72 + 108 + 48 = 228 sq in. Sarah makes the width 5 instead of 4. Her net has: 2(9×5) + 2(9×6) + 2(5×6) = 90 + 108 + 60 = 258 sq in. The width appears in 4 of the 6 faces (two 9×4 faces become 9×5, and two 4×6 faces become 5×6). Only the 9×6 faces remain unchanged.

The triangular prism has 5 faces: 2 triangular bases and 3 rectangular sides. Triangular bases: area = (1/2)(5)(12) = 30 sq cm each, so 2 × 30 = 60 sq cm total. For the rectangular sides, we need the lengths of all three sides of the triangle. The hypotenuse is √(5² + 12²) = √(25 + 144) = √169 = 13 cm. The three rectangular faces have areas: 5 × 8 = 40 sq cm, 12 × 8 = 96 sq cm, and 13 × 8 = 104 sq cm. Total surface area: 60 + 40 + 96 + 104 = 300 sq cm.

This question tests representing 3D figures with nets, which are unfolded 2D representations showing all faces, and using them to calculate surface area by summing the areas of rectangle and triangle faces. A net for a rectangular prism unfolds to 6 rectangles, surface area sums all; for 5×4×3 in, faces 5×4=20 (twice), 5×3=15 (twice), 4×3=12 (twice), total 2(20+15+12)=94 in². For example, adding only one of each like 20+15+12=47 in² counts just three faces, not all six. No, 47 in² is not the surface area because it counts only three faces; the correct is 94 in². A common error is this missing the opposite faces, or thinking nets overlap areas, or using cubic units like 94 in³ instead of in². To create a net, identify all six rectangles, arrange connected without overlap, label dimensions. To calculate, sum all face areas properly for 94 in²; in real life, this avoids underestimating material for a box.

This question tests representing 3D figures with nets, which are unfolded 2D representations showing all faces, and using them to calculate surface area by summing the areas of rectangle and triangle faces. A net for a rectangular prism unfolds to 6 rectangles, and surface area is the sum of all face areas; for a 3×4×5 cm prism, faces are 3×4=12 cm² (front/back, twice), 3×5=15 cm² (top/bottom, twice), 4×5=20 cm² (sides, twice), total 2(12+15+20)=94 cm², using A=lw for rectangles. For example, the net shows six rectangles (two 3×4, two 3×5, two 4×5), calculate 2×12 + 2×15 + 2×20 = 24 + 30 + 40 = 94 cm². The correct net includes all six faces, and the surface area is 94 cm². A common error is missing the pairs and adding only one of each, like 12+15+20=47 cm², or arithmetic mistakes leading to 90 or 60 cm², or using cm³ instead of cm². To create a net, identify the six rectangles in three equal pairs, arrange them connected flat, and label dimensions. To calculate, find each face type's area with A=lw, count two of each, sum all areas for 94 cm² in square units; in real life, this determines wrapping paper needed for the box.

This question tests representing 3D figures with nets, which are unfolded 2D representations showing all faces, and using them to calculate surface area by summing the areas of rectangle and triangle faces. A net for a cube unfolds to 6 squares, and surface area is the sum of all face areas; for an edge of 4 in, each square is 4×4=16 in², total 6×16=96 in², using A=lw for squares. For example, the net shows six congruent 4×4 squares, calculate 6×16=96 in². The correct net includes all six faces, and the surface area is 96 in². A common error is calculating only four faces like 4×16=64 in², or one face 16 in², or misadding to 80 in², or using in³ instead of in². To create a net, identify the six equal squares, arrange them connected flat without overlap, and label dimensions. To calculate, find the area of one square with A=lw, multiply by six for 96 in² in square units; in real life, this tells the material needed to cover a cube-shaped die or box.

This question tests representing 3D figures with nets, which are unfolded 2D patterns showing all faces, and using nets to calculate surface area by summing rectangle face areas. A net for this rectangular prism (4 cm × 4 cm × 6 cm) unfolds to two 4×4 squares and four 4×6 rectangles, with surface area summing all: 2(4×4)=32 cm² and 4(4×6)=96 cm², totaling 128 cm² using A=lw. For instance, like a cube but elongated, the net shows the squares as ends and rectangles as sides, summing to 128 cm². The correct surface area is 128 cm², accounting for the two square and four rectangular faces. A common error is treating it as a cube with six 4×4=96 cm², or forgetting two rectangles for 32+48=80 cm². To create a net, identify the faces (two squares, four rectangles), arrange connected flat, and label dimensions. To calculate, find areas, count multiples, sum with cm² units, useful for material coverage.

This question tests representing 3D figures with nets, which are unfolded 2D representations showing all faces, and using them to calculate surface area by summing the areas of rectangle and triangle faces. A net for a rectangular prism unfolds to 6 rectangles, and surface area is the sum of all face areas; for a 10×8×5 cm prism, faces are 10×8=80 cm² (twice), 10×5=50 cm² (twice), 8×5=40 cm² (twice), total 2(80+50+40)=340 cm², using A=lw for rectangles. For example, calculate 2×80 + 2×50 + 2×40 = 160 + 100 + 80 = 340 cm². The correct surface area for wrapping paper (all faces) is 340 cm². A common error is adding only one of each pair like 80+50+40=170 cm², or miscalculating pairs to 400 or 130 cm². To create a net, identify the six rectangles in three equal pairs, arrange connected flat, and label dimensions. To calculate, find each pair's area with A=lw, multiply by two, sum for 340 cm² in square units; in real life, this determines the paper needed to wrap a gift box without overlap.

This question tests representing 3D figures with nets, which are unfolded 2D patterns showing all faces, and using nets to calculate surface area by summing rectangle and triangle face areas. A net for a triangular prism unfolds to 2 triangles and 3 rectangles, with surface area as the sum of all; for example, bases with area (1/2)×6×4=12 m² each (24 m² total), and rectangles 6×10=60 m², 4×10=40 m², 5×10=50 m² (150 m² total), summing to 174 m² using A=(1/2)bh for triangles and A=lw for rectangles. For instance, the net shows two triangles (24 m²) and three distinct rectangles (150 m²), totaling 174 m². The correct surface area is 174 m², including both triangular bases and all lateral faces from the net. A common error is forgetting the (1/2) for triangles, using 6×4=24 m² each (48 m²) plus 150 m²=198 m², or missing one rectangle like omitting 50 m² for 124 m². To create a net, identify 2 triangles and 3 rectangles, arrange connected flat with the rectangles between the triangles' sides, and label dimensions. To calculate, find areas with appropriate formulas, count multiples, sum with m² units, useful for real-world like tent material.

Nets are used to represent 3D figures in 2D by unfolding them to show all faces, and we use them to calculate surface area by summing the areas of all the 2D shapes in the net. A net is the unfolded flat pattern of a 3D figure showing all its faces as 2D shapes; for example, a rectangular prism unfolds to 6 rectangles, and a triangular prism to 2 triangles and 3 rectangles. Surface area is the sum of the areas of all faces; for a rectangular prism with dimensions l,w,h, it's 2(lw + lh + wh). For example, for a rectangular prism 10×8×5, the net shows 6 rectangles (two 10×8=80, two 10×5=50, two 8×5=40), total surface area 2(80+50+40)=340. For this question, the correct net and surface area are a net with 6 rectangles; total area of paper needed =340 cm². Common errors include not multiplying by 2, adding overlaps, or using volume. To create a net, identify all 6 faces, arrange connected, label dimensions; to calculate, sum areas of all faces, use cm². Real-world uses include wrapping gifts without waste; avoid mistakes like missing pairs or wrong units.