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Rectangular Prism SA

Grade 6 · Geometry · Worksheet 3

  1. Aroha is designing a rectangular prism-shaped display case for a museum artifact. The case has a length of 18 centimeters, a width of 12 centimeters, and a height of 9 centimeters. She wants to cover the entire outside surface of the case (including the bottom) with a special protective film. What is the total surface area, in square centimeters, that needs to be covered?
    Answer: ______________
  2. A rectangular prism has length 28 cm, width 16 cm, and height 22 cm. Find its surface area.
    Answer: ______________
  3. Aroha is building a custom display case for her collection of hand-carved wooden birds. The case is a rectangular prism that measures 1.3 meters long, 0.9 meters wide, and 0.7 meters high. She wants to cover the entire exterior of the case with a special protective varnish, including the bottom. What is the total surface area of the display case in square meters? Answer: ______________
  4. 2³ × (15 - 7) + 4² = ? Answer: ______________
  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: ______________
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Answer Key & Explanations

Rectangular Prism SA · Grade 6 · Worksheet 3

  1. Aroha is designing a rectangular prism-shaped display case for a museum artifact. The case has a length of 18 centimeters, a width of 12 centimeters, and a height of 9 centimeters. She wants to cover the entire outside surface of the case (including the bottom) with a special protective film. What is the total surface area, in square centimeters, that needs to be covered? Answer: 972 Solution: Identify the dimensions. Length = 18 cm, Width = 12 cm, Height = 9 cm. Use the formula for surface area of a rectangular prism: SA = 2lw + 2lh + 2wh.
    Full step-by-step solution

    Step 1: Identify the dimensions. Length = 18 cm, Width = 12 cm, Height = 9 cm. Step 2: Use the formula for surface area of a rectangular prism: SA = 2lw + 2lh + 2wh. Step 3: Calculate the area of the top and bottom faces: 2 × (18 × 12) = 2 × 216 = 432 square centimeters. Step 4: Calculate the area of the front and back faces: 2 × (18 × 9) = 2 × 162 = 324 square centimeters. Step 5: Calculate the area of the left and right faces: 2 × (12 × 9) = 2 × 108 = 216 square centimeters. Step 6: Add all the areas together: 432 + 324 + 216 = 972 square centimeters. The total surface area to be covered is 972 square centimeters.

  2. A rectangular prism has length 28 cm, width 16 cm, and height 22 cm. Find its surface area. Answer: 2832 Solution: Write the formula: SA = 2lw + 2lh + 2wh Substitute the values: l = 28, w = 16, h = 22 Calculate 2lw = 2 × 28 × 16 = 2 × 448 = 896 Calculate 2lh = 2 × 28 × 22 = 2 × 616 = 1232 Calculate 2wh = 2 × 16 × 22 = 2 × 352 = 704 Add the three results: 896 + 1232 + 704 = 2832 The surface area is 2832…
    Full step-by-step solution

    Step 1: Write the formula: SA = 2lw + 2lh + 2wh Step 2: Substitute the values: l = 28, w = 16, h = 22 Step 3: Calculate 2lw = 2 × 28 × 16 = 2 × 448 = 896 Step 4: Calculate 2lh = 2 × 28 × 22 = 2 × 616 = 1232 Step 5: Calculate 2wh = 2 × 16 × 22 = 2 × 352 = 704 Step 6: Add the three results: 896 + 1232 + 704 = 2832 The surface area is 2832 square centimeters.

  3. Aroha is building a custom display case for her collection of hand-carved wooden birds. The case is a rectangular prism that measures 1.3 meters long, 0.9 meters wide, and 0.7 meters high. She wants to cover the entire exterior of the case with a special protective varnish, including the bottom. What is the total surface area of the display case in square meters? Answer: 5.42 Solution: Identify the dimensions: length (l) = 1.3 m, width (w) = 0.9 m, height (h) = 0.7 m. Calculate the area of the front and back faces: 2 × (l × h) = 2 × (1.3 × 0.7) = 2 × 0.91 = 1.82 m².
    Full step-by-step solution

    Step 1: Identify the dimensions: length (l) = 1.3 m, width (w) = 0.9 m, height (h) = 0.7 m. Step 2: Calculate the area of the front and back faces: 2 × (l × h) = 2 × (1.3 × 0.7) = 2 × 0.91 = 1.82 m². Step 3: Calculate the area of the left and right faces: 2 × (w × h) = 2 × (0.9 × 0.7) = 2 × 0.63 = 1.26 m². Step 4: Calculate the area of the top and bottom faces: 2 × (l × w) = 2 × (1.3 × 0.9) = 2 × 1.17 = 2.34 m². Step 5: Add all the areas together: 1.82 + 1.26 + 2.34 = 5.42 m². The total surface area of the display case is 5.42 square meters.

  4. 2³ × (15 - 7) + 4² = ? Answer: 80 Solution: 2³ × (15 - 7) + 4² Handle exponents first. 2³ means 2 × 2 × 2 = 8 4² means 4 × 4 = 16 So now we have: 8 × (15 - 7) + 16 Evaluate inside parentheses. 15 - 7 = 8 Now we have: 8 × 8 + 16 Perform multiplication.
    Full step-by-step solution

    Let's solve step by step using the order of operations (PEMDAS/BODMAS). Step 1: Identify the expression: 2³ × (15 - 7) + 4² Step 2: Handle exponents first. 2³ means 2 × 2 × 2 = 8 4² means 4 × 4 = 16 So now we have: 8 × (15 - 7) + 16 Step 3: Evaluate inside parentheses. 15 - 7 = 8 Now we have: 8 × 8 + 16 Step 4: Perform multiplication. 8 × 8 = 64 Now we have: 64 + 16 Step 5: Perform addition. 64 + 16 = 80 Final answer: 80

  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.