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Rectangular Prism SA

Grade 6 · Geometry · Worksheet 1

  1. A rectangular prism has length 14 cm, width 9 cm, and height 11 cm. Find its surface area.
    Answer: ______________
  2. Emma is wrapping a rectangular prism-shaped gift box with no top. The box has a length of 35 cm, a width of 25 cm, and a height of 15 cm. She will cover all the outside surfaces except the top opening. What is the total surface area Emma will wrap in square centimeters?
    Answer: ______________
  3. Mason is building a large storage chest for his camping gear. The chest is a rectangular prism that measures 1.7 meters long, 0.7 meters wide, and 0.5 meters high. He wants to paint the entire exterior, including the bottom and the lid. How many square meters of surface does Mason need to paint? Answer: ______________
  4. 2³ × (18 - 6) + 144 ÷ 12 = ? Answer: ______________
  5. 2³ × (15 - 7) + 24 ÷ 3 = ? Answer: ______________
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Answer Key & Explanations

Rectangular Prism SA · Grade 6 · Worksheet 1

  1. A rectangular prism has length 14 cm, width 9 cm, and height 11 cm. Find its surface area. Answer: 758 Solution: Write the formula: SA = 2lw + 2lh + 2wh Substitute the given values: l = 14, w = 9, h = 11 Calculate lw: 14 × 9 = 126 Calculate lh: 14 × 11 = 154 Calculate wh: 9 × 11 = 99 Multiply each by 2: 2 × 126 = 252, 2 × 154 = 308, 2 × 99 = 198 Add the three results: 252 + 308 = 560, then 560 + 198 = 758…
    Full step-by-step solution

    Step 1: Write the formula: SA = 2lw + 2lh + 2wh Step 2: Substitute the given values: l = 14, w = 9, h = 11 Step 3: Calculate lw: 14 × 9 = 126 Step 4: Calculate lh: 14 × 11 = 154 Step 5: Calculate wh: 9 × 11 = 99 Step 6: Multiply each by 2: 2 × 126 = 252, 2 × 154 = 308, 2 × 99 = 198 Step 7: Add the three results: 252 + 308 = 560, then 560 + 198 = 758 The answer is 758.

  2. Emma is wrapping a rectangular prism-shaped gift box with no top. The box has a length of 35 cm, a width of 25 cm, and a height of 15 cm. She will cover all the outside surfaces except the top opening. What is the total surface area Emma will wrap in square centimeters? Answer: 2675 Solution: Identify the five faces to cover (all except the top). Calculate the area of the bottom (length × width): 35 × 25 = 875 square cm.
    Full step-by-step solution

    Step 1: Identify the five faces to cover (all except the top). Step 2: Calculate the area of the bottom (length × width): 35 × 25 = 875 square cm. Step 3: Calculate the area of the two longer side walls (length × height): each is 35 × 15 = 525 square cm. Two of them: 525 × 2 = 1050 square cm. Step 4: Calculate the area of the two shorter side walls (width × height): each is 25 × 15 = 375 square cm. Two of them: 375 × 2 = 750 square cm. Step 5: Add all the areas together: 875 + 1050 + 750 = 2675 square cm. The total surface area Emma will wrap is 2675 square centimeters.

  3. Mason is building a large storage chest for his camping gear. The chest is a rectangular prism that measures 1.7 meters long, 0.7 meters wide, and 0.5 meters high. He wants to paint the entire exterior, including the bottom and the lid. How many square meters of surface does Mason need to paint? Answer: 4.78 Solution: Identify the dimensions: length (l) = 1.7 m, width (w) = 0.7 m, height (h) = 0.5 m. Calculate the area of the top and bottom faces: 2 × (l × w) = 2 × (1.7 × 0.7) = 2 × 1.19 = 2.38 m².
    Full step-by-step solution

    Step 1: Identify the dimensions: length (l) = 1.7 m, width (w) = 0.7 m, height (h) = 0.5 m. Step 2: Calculate the area of the top and bottom faces: 2 × (l × w) = 2 × (1.7 × 0.7) = 2 × 1.19 = 2.38 m². Step 3: Calculate the area of the front and back faces: 2 × (l × h) = 2 × (1.7 × 0.5) = 2 × 0.85 = 1.70 m². Step 4: Calculate the area of the left and right faces: 2 × (w × h) = 2 × (0.7 × 0.5) = 2 × 0.35 = 0.70 m². Step 5: Add all the areas together: 2.38 + 1.70 + 0.70 = 4.78 m². The total surface area Mason needs to paint is 4.78 square meters.

  4. 2³ × (18 - 6) + 144 ÷ 12 = ? Answer: 108 Solution: Calculate inside the parentheses: 18 - 6 = 12 Calculate the exponent: 2³ = 2 × 2 × 2 = 8 Multiply the results: 8 × 12 = 96 Perform the division: 144 ÷ 12 = 12 Add the results: 96 + 12 = 108 The answer is 108.
    Full step-by-step solution

    Step 1: Calculate inside the parentheses: 18 - 6 = 12 Step 2: Calculate the exponent: 2³ = 2 × 2 × 2 = 8 Step 3: Multiply the results: 8 × 12 = 96 Step 4: Perform the division: 144 ÷ 12 = 12 Step 5: Add the results: 96 + 12 = 108 The answer is 108.

  5. 2³ × (15 - 7) + 24 ÷ 3 = ? Answer: 72 Solution: Handle the exponent first. 2³ means 2 × 2 × 2 = 8. 8 × (15 - 7) + 24 ÷ 3 Evaluate inside the parentheses.
    Full step-by-step solution

    Let's solve step by step using the order of operations (PEMDAS/BODMAS). Step 1: Handle the exponent first. 2³ means 2 × 2 × 2 = 8. So the expression becomes: 8 × (15 - 7) + 24 ÷ 3 Step 2: Evaluate inside the parentheses. 15 - 7 = 8 Now we have: 8 × 8 + 24 ÷ 3 Step 3: Perform multiplication and division from left to right. First, 8 × 8 = 64 Then, 24 ÷ 3 = 8 Now we have: 64 + 8 Step 4: Perform addition. 64 + 8 = 72 Final answer: 72