Rectangular Prism SA

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Answer Key & Explanations

Rectangular Prism SA · Grade 6 · Worksheet 1

1. A shipping container has dimensions 15 m by 8 m by 6 m. What is its total surface area? Answer: 516 Solution: Identify the dimensions: length (l) = 15 m, width (w) = 8 m, height (h) = 6 m. Use the formula SA = 2lw + 2lh + 2wh. Calculate 2lw = 2 × 15 × 8 = 2 × 120 = 240.
   Full step-by-step solution

   Step 1: Identify the dimensions: length (l) = 15 m, width (w) = 8 m, height (h) = 6 m. Step 2: Use the formula SA = 2lw + 2lh + 2wh. Step 3: Calculate 2lw = 2 × 15 × 8 = 2 × 120 = 240. Step 4: Calculate 2lh = 2 × 15 × 6 = 2 × 90 = 180. Step 5: Calculate 2wh = 2 × 8 × 6 = 2 × 48 = 96. Step 6: Add the three areas: 240 + 180 + 96 = 516. The total surface area is 516 square meters.

2. A rectangular prism has dimensions: l = 14 cm, w = 10 cm, h = 8 cm. Find its surface area. Answer: 664 Solution: Write the formula: SA = 2lw + 2lh + 2wh Substitute the given values: l = 14, w = 10, h = 8 Calculate lw: 14 × 10 = 140. Then 2lw = 2 × 140 = 280 Calculate lh: 14 × 8 = 112.
   Full step-by-step solution

   Step 1: Write the formula: SA = 2lw + 2lh + 2wh Step 2: Substitute the given values: l = 14, w = 10, h = 8 Step 3: Calculate lw: 14 × 10 = 140. Then 2lw = 2 × 140 = 280 Step 4: Calculate lh: 14 × 8 = 112. Then 2lh = 2 × 112 = 224 Step 5: Calculate wh: 10 × 8 = 80. Then 2wh = 2 × 80 = 160 Step 6: Add all three: 280 + 224 + 160 = 664 The answer is 664.

3. Isabella is designing a shipping crate in the shape of a rectangular prism. The crate has a length of 8 feet, a width of 5 feet, and a height of 4 feet. She needs to cover all six faces of the crate with a special waterproof coating. What is the total surface area she needs to cover, in square feet? Answer: 184 Solution: Identify the dimensions: length (l) = 8 ft, width (w) = 5 ft, height (h) = 4 ft. Calculate the area of the top and bottom faces (each is l x w): Area of one top/bottom face = 8 x 5 = 40 square feet.
   Full step-by-step solution

   Step 1: Identify the dimensions: length (l) = 8 ft, width (w) = 5 ft, height (h) = 4 ft. Step 2: Calculate the area of the top and bottom faces (each is l x w): Area of one top/bottom face = 8 x 5 = 40 square feet. Two such faces: 2 x 40 = 80 square feet. Step 3: Calculate the area of the front and back faces (each is l x h): Area of one front/back face = 8 x 4 = 32 square feet. Two such faces: 2 x 32 = 64 square feet. Step 4: Calculate the area of the left and right faces (each is w x h): Area of one left/right face = 5 x 4 = 20 square feet. Two such faces: 2 x 20 = 40 square feet. Step 5: Add all the areas together: 80 + 64 + 40 = 184 square feet. The total surface area of the crate is 184 square feet.

4. Liam is wrapping a gift box for his friend's birthday. The box is 24 cm long, 18 cm wide, and 12 cm high. He needs to calculate the total surface area to determine how much wrapping paper to buy. What is the total surface area of the box in square centimeters? Answer: 1872 Solution: Length (L) = 24 cm Width (W) = 18 cm Height (H) = 12 cm The total surface area is the sum of the areas of all 6 faces. Identify the faces.
   Full step-by-step solution

   Let's find the total surface area of the box step by step. Step 1: Understand the problem. The box is a rectangular prism with: Length (L) = 24 cm Width (W) = 18 cm Height (H) = 12 cm The total surface area is the sum of the areas of all 6 faces. Step 2: Identify the faces. A rectangular prism has three pairs of identical faces: - Top and bottom: area = L × W (each) - Front and back: area = L × H (each) - Left and right: area = W × H (each) Step 3: Calculate the area of each pair. Area of top and bottom together = 2 × (L × W) = 2 × (24 × 18) 24 × 18 = 432 So 2 × 432 = 864 cm² Area of front and back together = 2 × (L × H) = 2 × (24 × 12) 24 × 12 = 288 So 2 × 288 = 576 cm² Area of left and right together = 2 × (W × H) = 2 × (18 × 12) 18 × 12 = 216 So 2 × 216 = 432 cm² Step 4: Add them up for total surface area. Total surface area = 864 + 576 + 432 First: 864 + 576 = 1440 Then: 1440 + 432 = 1872 Step 5: State the final answer. The total surface area of the box is 1872 square centimeters.

5. Carlos is building a custom display case for his rock collection. The case is a rectangular prism that measures 1.5 meters long, 0.8 meters wide, and 0.6 meters high. He needs to cover all exterior surfaces with protective glass panels. What is the total surface area of the display case in square meters? Answer: 5.16 Solution: Identify the dimensions: length = 1.5 m, width = 0.8 m, height = 0.6 m Calculate area of front and back faces: 2 × (1.5 × 0.6) = 2 × 0.9 = 1.8 m² Calculate area of left and right faces: 2 × (0.8 × 0.6) = 2 × 0.48 = 0.96 m² Calculate area of top and bottom faces: 2 × (1.5 × 0.8) = 2 × 1.2 = 2.4…
   Full step-by-step solution

   Step 1: Identify the dimensions: length = 1.5 m, width = 0.8 m, height = 0.6 m Step 2: Calculate area of front and back faces: 2 × (1.5 × 0.6) = 2 × 0.9 = 1.8 m² Step 3: Calculate area of left and right faces: 2 × (0.8 × 0.6) = 2 × 0.48 = 0.96 m² Step 4: Calculate area of top and bottom faces: 2 × (1.5 × 0.8) = 2 × 1.2 = 2.4 m² Step 5: Add all areas together: 1.8 + 0.96 + 2.4 = 5.16 m² The total surface area is 5.16 square meters.