Surface Area and Nets Test Answer Key with Scoring – Grade 6

Question 1 Surface area of a carton (2 points)

2(7 × 3) = 42, 2(7 × 5) = 70, 2(3 × 5) = 30. SA = 42 + 70 + 30 = 142.

142 square inches

Scoring: 1 point for the three pair areas, 1 point for the total with square units.

Question 2 Triangular prism (3 points)

Triangles: 2 × (12 × 7 × 24) = 168. Rectangles: (7 + 24 + 25) × 12 = 56 × 12 = 672. Total: 168 + 672 = 840.

840 square centimeters

Scoring: 1 point for the triangles, 1 point for the rectangles, 1 point for the total with units.

Question 3 Cube (2 points)

One face: 15 × 15 = 225. Six faces: 6 × 225 = 1,350.

1,350 square centimeters

Scoring: 1 point for a face area of 225, 1 point for the total.

Question 4 Square pyramid (3 points)

Base: 9 × 9 = 81. Triangle: 12 × 9 × 11 = 49.5. Four triangles: 198. Total: 81 + 198 = 279.

279 square inches

Scoring: 1 point for the base, 1 point for the four triangles, 1 point for the total with units.

Question 5 Pet crate without a lid (3 points)

1. 30 × 20 = 600 square inches.
2. 2(30 × 18) + 2(20 × 18) = 1,080 + 720 = 1,800 square inches.
3. 600 + 1,800 = 2,400 square inches.

Scoring: 1 point for each part.

Question 6 Wrapping a box (3 points)

1. 2(12 × 9) + 2(12 × 5) + 2(9 × 5) = 216 + 120 + 90 = 426 square inches.
2. 426 ÷ 300 = 1.42, so 2 sheets.

Scoring: 2 points for part (a), with 1 point for correct pair areas; 1 point for rounding up to 2.

Question 7 Missing height (2 points)

122 = 2(11 × 3) + 2(11h) + 2(3h) = 66 + 28h. Then 28h = 56, so h = 2. Check: 2(33 + 22 + 6) = 122.

2 inches

Scoring: 1 point for the equation, 1 point for the answer.

Question 8 Name the solid (2 points)

1. A square base with four triangles is a square pyramid.
2. The base has 4 edges and 4 more edges go up to the top, so 8 edges.

Scoring: 1 point for each part.