Surface Area Nets

lessonbunny.com

Answer Key & Explanations

Surface Area Nets · Grade 6 · Worksheet 1

1. A net of a rectangular prism has faces with dimensions: two faces are 20 cm by 15 cm, two faces are 20 cm by 10 cm, and two faces are 15 cm by 10 cm. What is the total surface area of the prism? Answer: 1300 Solution: Identify the three different face sizes and their areas. - Two faces are 20 cm by 15 cm: area of one = 20 × 15 = 300 square cm. Two faces = 2 × 300 = 600 square cm.
   Full step-by-step solution

   Step 1: Identify the three different face sizes and their areas. - Two faces are 20 cm by 15 cm: area of one = 20 × 15 = 300 square cm. Two faces = 2 × 300 = 600 square cm. - Two faces are 20 cm by 10 cm: area of one = 20 × 10 = 200 square cm. Two faces = 2 × 200 = 400 square cm. - Two faces are 15 cm by 10 cm: area of one = 15 × 10 = 150 square cm. Two faces = 2 × 150 = 300 square cm. Step 2: Add the areas of all six faces: 600 + 400 + 300 = 1300 square cm. The total surface area is 1300 square cm.

2. A net of a rectangular prism has faces with dimensions: two faces are 15 cm by 9 cm, two faces are 15 cm by 11 cm, and two faces are 9 cm by 11 cm. What is the total surface area of the prism? Answer: 798 Solution: Identify the three pairs of identical faces. Pair 1: 15 cm by 9 cm. Area of one face = 15 × 9 = 135 square cm.
   Full step-by-step solution

   Step 1: Identify the three pairs of identical faces. Pair 1: 15 cm by 9 cm. Area of one face = 15 × 9 = 135 square cm. Two faces = 2 × 135 = 270 square cm. Step 2: Pair 2: 15 cm by 11 cm. Area of one face = 15 × 11 = 165 square cm. Two faces = 2 × 165 = 330 square cm. Step 3: Pair 3: 9 cm by 11 cm. Area of one face = 9 × 11 = 99 square cm. Two faces = 2 × 99 = 198 square cm. Step 4: Add all areas: 270 + 330 + 198 = 798 square cm. The answer is 798.

3. A net of a rectangular prism has faces with dimensions: 14 cm by 11 cm, 14 cm by 9 cm, 11 cm by 9 cm, each appearing twice. What is the total surface area in square centimeters? Answer: 758 Solution: Identify the three unique rectangles from the net: 14 cm by 11 cm, 14 cm by 9 cm, and 11 cm by 9 cm. Calculate the area of the first rectangle: 14 × 11 = 154 square cm.
   Full step-by-step solution

   Step 1: Identify the three unique rectangles from the net: 14 cm by 11 cm, 14 cm by 9 cm, and 11 cm by 9 cm. Step 2: Calculate the area of the first rectangle: 14 × 11 = 154 square cm. Step 3: Calculate the area of the second rectangle: 14 × 9 = 126 square cm. Step 4: Calculate the area of the third rectangle: 11 × 9 = 99 square cm. Step 5: Since each rectangle appears twice in the net, multiply each area by 2: 2 × 154 = 308, 2 × 126 = 252, 2 × 99 = 198. Step 6: Add the doubled areas: 308 + 252 + 198 = 758. The total surface area is 758 square centimeters.

4. Noah is designing a custom display box for a museum. The box is shaped like a rectangular prism. He draws a net of the box on grid paper. The net shows that the box has a rectangular base measuring 16 cm by 11 cm, two side faces that are 16 cm by 6 cm, and two end faces that are 11 cm by 6 cm. Noah needs to calculate the total surface area to know how much special protective coating to buy for all the exterior surfaces. What is the total surface area of Noah's display box in square centimeters? Answer: 676 Solution: Identify the three pairs of faces. - Top and bottom: each is 16 cm by 11 cm - Front and back: each is 16 cm by 6 cm - Left and right ends: each is 11 cm by 6 cm Find the area of one top/bottom face.
   Full step-by-step solution

   Step 1: Identify the three pairs of faces. - Top and bottom: each is 16 cm by 11 cm - Front and back: each is 16 cm by 6 cm - Left and right ends: each is 11 cm by 6 cm Step 2: Find the area of one top/bottom face. 16 x 11 = 176 square cm Two faces: 2 x 176 = 352 square cm Step 3: Find the area of one front/back face. 16 x 6 = 96 square cm Two faces: 2 x 96 = 192 square cm Step 4: Find the area of one left/right end face. 11 x 6 = 66 square cm Two faces: 2 x 66 = 132 square cm Step 5: Add all the areas together. 352 + 192 + 132 = 676 square cm The total surface area is 676 square centimeters.

5. Emma is designing a custom display case for her collection of seashells. She draws a net of a rectangular prism on cardboard. The net consists of six rectangles: two are 25 cm by 15 cm, two are 25 cm by 20 cm, and two are 15 cm by 20 cm. Emma needs to calculate the total surface area to know how much clear plastic she needs to cover all the outside faces. What is the total surface area of Emma's display case in square centimeters? Answer: 2350 Solution: Find the area of one 25 cm by 15 cm face: 25 × 15 = 375 square cm. There are two such faces, so total = 2 × 375 = 750 square cm. Find the area of one 25 cm by 20 cm face: 25 × 20 = 500 square cm.
   Full step-by-step solution

   Step 1: Find the area of one 25 cm by 15 cm face: 25 × 15 = 375 square cm. There are two such faces, so total = 2 × 375 = 750 square cm. Step 2: Find the area of one 25 cm by 20 cm face: 25 × 20 = 500 square cm. There are two such faces, so total = 2 × 500 = 1000 square cm. Step 3: Find the area of one 15 cm by 20 cm face: 15 × 20 = 300 square cm. There are two such faces, so total = 2 × 300 = 600 square cm. Step 4: Add all the face areas together: 750 + 1000 + 600 = 2350 square cm. The total surface area is 2350 square centimeters.

6. A net of a rectangular prism shows faces with dimensions 14 cm by 9 cm, 14 cm by 11 cm, and 9 cm by 11 cm. What is the surface area of the prism? Answer: 758 Solution: Identify the three different pairs of faces. The dimensions are 14 cm by 9 cm, 14 cm by 11 cm, and 9 cm by 11 cm. Each appears twice.
   Full step-by-step solution

   Step 1: Identify the three different pairs of faces. The dimensions are 14 cm by 9 cm, 14 cm by 11 cm, and 9 cm by 11 cm. Each appears twice. Step 2: Calculate the area of the first pair: 14 × 9 = 126 square cm. Two faces: 2 × 126 = 252 square cm. Step 3: Calculate the area of the second pair: 14 × 11 = 154 square cm. Two faces: 2 × 154 = 308 square cm. Step 4: Calculate the area of the third pair: 9 × 11 = 99 square cm. Two faces: 2 × 99 = 198 square cm. Step 5: Add all areas: 252 + 308 + 198 = 758 square cm. The answer is 758.