Rectangular Prism SA

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Rectangular Prism SA · Grade 6 · Worksheet 2

1. Mere is building a custom rectangular prism-shaped shipping crate to send her handmade quilts to an international exhibition. The crate has a length of 2200 mm, a width of 1600 mm, and a height of 1400 mm. She needs to cover all six exterior faces with a special protective sealant. What is the total surface area of the crate in square millimeters? Answer: 17680000 Solution: Identify the dimensions: length (l) = 2200 mm, width (w) = 1600 mm, height (h) = 1400 mm. Calculate the area of the front face (length x height): 2200 x 1400 = 3,080,000 mm².
   Full step-by-step solution

   Step 1: Identify the dimensions: length (l) = 2200 mm, width (w) = 1600 mm, height (h) = 1400 mm. Step 2: Calculate the area of the front face (length x height): 2200 x 1400 = 3,080,000 mm². The back face is identical, so both together: 2 x 3,080,000 = 6,160,000 mm². Step 3: Calculate the area of the side face (width x height): 1600 x 1400 = 2,240,000 mm². The opposite side is identical, so both together: 2 x 2,240,000 = 4,480,000 mm². Step 4: Calculate the area of the top face (length x width): 2200 x 1600 = 3,520,000 mm². The bottom face is identical, so both together: 2 x 3,520,000 = 7,040,000 mm². Step 5: Add all three doubled areas together: 6,160,000 + 4,480,000 + 7,040,000 = 17,680,000 mm². The total surface area of the crate is 17,680,000 square millimeters.

2. Noah is building a large storage crate in the shape of a rectangular prism. The crate has a length of 1200 mm, a width of 800 mm, and a height of 600 mm. He wants to cover all six faces with weatherproof fabric. What is the total surface area of the crate in square meters? Answer: 4.32 Solution: Identify the dimensions: length (l) = 1200 mm, width (w) = 800 mm, height (h) = 600 mm. Use the surface area formula for a rectangular prism: SA = 2lw + 2lh + 2wh.
   Full step-by-step solution

   Step 1: Identify the dimensions: length (l) = 1200 mm, width (w) = 800 mm, height (h) = 600 mm. Step 2: Use the surface area formula for a rectangular prism: SA = 2lw + 2lh + 2wh. Step 3: Calculate the area of the top and bottom faces (lw): 1200 × 800 = 960,000 square mm. Two faces: 2 × 960,000 = 1,920,000 square mm. Step 4: Calculate the area of the front and back faces (lh): 1200 × 600 = 720,000 square mm. Two faces: 2 × 720,000 = 1,440,000 square mm. Step 5: Calculate the area of the left and right faces (wh): 800 × 600 = 480,000 square mm. Two faces: 2 × 480,000 = 960,000 square mm. Step 6: Add all the areas: 1,920,000 + 1,440,000 + 960,000 = 4,320,000 square mm. Step 7: Convert square millimeters to square meters. Since 1 m = 1000 mm, then 1 square meter = 1,000,000 square mm. Divide: 4,320,000 ÷ 1,000,000 = 4.32 square meters. The answer is 4.32.

3. Aisha is designing a custom wooden crate to ship her pottery collection. The crate is a rectangular prism that measures 3.2 feet long, 2.1 feet wide, and 1.8 feet high. She needs to calculate the total surface area to determine how much protective coating to buy for the entire exterior, including the bottom. What is the total surface area of the crate in square feet? Answer: 32.52 Solution: Identify the dimensions: length = 3.2 ft, width = 2.1 ft, height = 1.8 ft Calculate area of front and back faces: 2 × (length × height) = 2 × (3.2 × 1.8) = 2 × 5.76 = 11.52 sq ft Calculate area of left and right faces: 2 × (width × height) = 2 × (2.1 × 1.8) = 2 × 3.78 = 7.56 sq ft Calculate area…
   Full step-by-step solution

   Step 1: Identify the dimensions: length = 3.2 ft, width = 2.1 ft, height = 1.8 ft Step 2: Calculate area of front and back faces: 2 × (length × height) = 2 × (3.2 × 1.8) = 2 × 5.76 = 11.52 sq ft Step 3: Calculate area of left and right faces: 2 × (width × height) = 2 × (2.1 × 1.8) = 2 × 3.78 = 7.56 sq ft Step 4: Calculate area of top and bottom faces: 2 × (length × width) = 2 × (3.2 × 2.1) = 2 × 6.72 = 13.44 sq ft Step 5: Add all areas together: 11.52 + 7.56 + 13.44 = 32.52 sq ft The total surface area is 32.52 square feet.

4. Carlos is building a custom wooden bookshelf for his classroom. The bookshelf is a rectangular prism that measures 2.4 meters long, 0.8 meters wide, and 1.6 meters high. He needs to calculate the total exterior surface area to determine how much wood stain to purchase for all six faces. What is the total surface area of the bookshelf in square meters? Answer: 14.08 Solution: Identify the dimensions: length = 2.4 m, width = 0.8 m, height = 1.6 m Calculate the area of the front and back faces: 2 × (length × height) = 2 × (2.4 × 1.6) = 2 × 3.84 = 7.68 m² Calculate the area of the left and right faces: 2 × (width × height) = 2 × (0.8 × 1.6) = 2 × 1.28 = 2.56 m²…
   Full step-by-step solution

   Step 1: Identify the dimensions: length = 2.4 m, width = 0.8 m, height = 1.6 m Step 2: Calculate the area of the front and back faces: 2 × (length × height) = 2 × (2.4 × 1.6) = 2 × 3.84 = 7.68 m² Step 3: Calculate the area of the left and right faces: 2 × (width × height) = 2 × (0.8 × 1.6) = 2 × 1.28 = 2.56 m² Step 4: Calculate the area of the top and bottom faces: 2 × (length × width) = 2 × (2.4 × 0.8) = 2 × 1.92 = 3.84 m² Step 5: Add all the areas together: 7.68 + 2.56 + 3.84 = 14.08 m² The total surface area is 14.08 square meters.