Surface Area Nets

lessonbunny.com

Answer Key & Explanations

Surface Area Nets · Grade 6 · Worksheet 3

1. Maria is designing a custom storage container for her art supplies. The container is shaped like a rectangular prism with length 18 cm, width 12 cm, and height 15 cm. She needs to calculate the total surface area to determine how much decorative contact paper she needs to cover all the outside faces. What is the total surface area of the container in square centimeters? Answer: 1332 Solution: Identify the dimensions: length = 18 cm, width = 12 cm, height = 15 cm Calculate area of front and back faces: 2 × (length × height) = 2 × (18 × 15) = 2 × 270 = 540 cm² Calculate area of left and right faces: 2 × (width × height) = 2 × (12 × 15) = 2 × 180 = 360 cm² Calculate area of top and…
   Full step-by-step solution

   Step 1: Identify the dimensions: length = 18 cm, width = 12 cm, height = 15 cm Step 2: Calculate area of front and back faces: 2 × (length × height) = 2 × (18 × 15) = 2 × 270 = 540 cm² Step 3: Calculate area of left and right faces: 2 × (width × height) = 2 × (12 × 15) = 2 × 180 = 360 cm² Step 4: Calculate area of top and bottom faces: 2 × (length × width) = 2 × (18 × 12) = 2 × 216 = 432 cm² Step 5: Add all areas together: 540 + 360 + 432 = 1332 cm² The total surface area is 1332 square centimeters.

2. Maria is designing a custom gift box for her friend's birthday. The box is shaped like a rectangular prism with a length of 18 cm, a width of 12 cm, and a height of 10 cm. She needs to calculate the total surface area to know how much decorative paper she needs to cover all the outside faces. What is the total surface area of the box in square centimeters? Answer: 1032 Solution: Identify the three pairs of faces. Pair 1: Front and Back (length x height) = 18 cm x 10 cm Pair 2: Left and Right (width x height) = 12 cm x 10 cm Pair 3: Top and Bottom (length x width) = 18 cm x 12 cm Calculate the area for one face of each pair.
   Full step-by-step solution

   Step 1: Identify the three pairs of faces. Pair 1: Front and Back (length x height) = 18 cm x 10 cm Pair 2: Left and Right (width x height) = 12 cm x 10 cm Pair 3: Top and Bottom (length x width) = 18 cm x 12 cm Step 2: Calculate the area for one face of each pair. Area of one Front/Back face = 18 * 10 = 180 cm² Area of one Left/Right face = 12 * 10 = 120 cm² Area of one Top/Bottom face = 18 * 12 = 216 cm² Step 3: Since there are two of each face, multiply each area by 2. Total area for Front/Back = 180 * 2 = 360 cm² Total area for Left/Right = 120 * 2 = 240 cm² Total area for Top/Bottom = 216 * 2 = 432 cm² Step 4: Add all the total areas together to find the surface area. Surface Area = 360 + 240 + 432 = 1032 cm² The answer is 1032.

3. A net of a rectangular prism is shown. The net has two faces that are 15 cm by 11 cm, two faces that are 15 cm by 9 cm, and two faces that are 11 cm by 9 cm. What is the surface area of the rectangular prism? Answer: 798 Solution: Identify the three different rectangle sizes from the net. - Two faces are 15 cm by 11 cm. - Two faces are 15 cm by 9 cm.
   Full step-by-step solution

   Step 1: Identify the three different rectangle sizes from the net. - Two faces are 15 cm by 11 cm. - Two faces are 15 cm by 9 cm. - Two faces are 11 cm by 9 cm. Step 2: Calculate the area of each rectangle. Area of 15 cm by 11 cm = 15 × 11 = 165 square cm. Area of 15 cm by 9 cm = 15 × 9 = 135 square cm. Area of 11 cm by 9 cm = 11 × 9 = 99 square cm. Step 3: Multiply each area by 2 (since there are two of each). 2 × 165 = 330 square cm. 2 × 135 = 270 square cm. 2 × 99 = 198 square cm. Step 4: Add all the areas together. 330 + 270 + 198 = 798 square cm. The surface area of the rectangular prism is 798 square cm.

4. 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.

5. 2³ × (15 - 7) + √144 = ? Answer: 76 Solution: 2³ × (15 - 7) + √144 2³ means 2 × 2 × 2 = 8 So now we have: 8 × (15 - 7) + √144 15 - 7 = 8 So now: 8 × 8 + √144 √144 = 12 (since 12 × 12 = 144) So now: 8 × 8 + 12 8 × 8 = 64 So now: 64 + 12 64 + 12 = 76 Final Answer: 76
   Full step-by-step solution

   Let's solve step by step. We have: 2³ × (15 - 7) + √144 **Step 1: Handle the exponent** 2³ means 2 × 2 × 2 = 8 So now we have: 8 × (15 - 7) + √144 **Step 2: Simplify inside parentheses** 15 - 7 = 8 So now: 8 × 8 + √144 **Step 3: Handle the square root** √144 = 12 (since 12 × 12 = 144) So now: 8 × 8 + 12 **Step 4: Perform multiplication** 8 × 8 = 64 So now: 64 + 12 **Step 5: Perform addition** 64 + 12 = 76 **Final Answer:** 76