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3D Volume and Surface

Grade 7 · Geometry · Worksheet 3

  1. Aisha is building a rectangular prism-shaped planter box for her school garden. The box needs to hold 12,000 cubic centimeters of soil. If the length is 40 cm and the width is 25 cm, what height should Aisha make the planter box?
    Answer: ______________
  2. A rectangular prism has dimensions 35 cm × 25 cm × 20 cm. Calculate its volume and total surface area. (Format: Volume = ? cm³, Surface Area = ? cm²)
    Answer: ______________
  3. A rectangular prism has length 15 cm, width 10 cm, and height 8 cm. Calculate its volume and surface area. (Format: Volume = ? cm³, Surface Area = ? cm²)
    Answer: ______________
  4. Mason is designing a cylindrical storage tank for his family's rainwater collection system. The tank needs to hold exactly 17,000 liters of water and has a height of 2.7 meters. What is the radius of the tank's circular base? Use π ≈ 3.14 and round your answer to the nearest tenth of a meter. (Remember: 1 cubic meter = 1000 liters) Answer: ______________
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Answer Key & Explanations

3D Volume and Surface · Grade 7 · Worksheet 3

  1. Aisha is building a rectangular prism-shaped planter box for her school garden. The box needs to hold 12,000 cubic centimeters of soil. If the length is 40 cm and the width is 25 cm, what height should Aisha make the planter box? Answer: 12 Solution: The formula for volume of a rectangular prism is: Volume = length × width × height We know: Volume = 12,000 cm³, length = 40 cm, width = 25 cm Substitute the known values: 12,000 = 40 × 25 × height Calculate 40 × 25 = 1,000 So 12,000 = 1,000 × height Divide both sides by 1,000: height = 12,000 ÷…
    Full step-by-step solution

    Step 1: The formula for volume of a rectangular prism is: Volume = length × width × height Step 2: We know: Volume = 12,000 cm³, length = 40 cm, width = 25 cm Step 3: Substitute the known values: 12,000 = 40 × 25 × height Step 4: Calculate 40 × 25 = 1,000 Step 5: So 12,000 = 1,000 × height Step 6: Divide both sides by 1,000: height = 12,000 ÷ 1,000 Step 7: height = 12 cm The answer is 12 cm.

  2. A rectangular prism has dimensions 35 cm × 25 cm × 20 cm. Calculate its volume and total surface area. (Format: Volume = ? cm³, Surface Area = ? cm²) Answer: Volume = 17500 cm³, Surface Area = 4150 cm² Solution: Calculate the volume using V = l × w × h V = 35 × 25 × 20 V = 875 × 20 V = 17500 cm³ Calculate the surface area using SA = 2(lw + lh + wh) First, lw = 35 × 25 = 875 cm² Next, lh = 35 × 20 = 700 cm² Then, wh = 25 × 20 = 500 cm² Now add: 875 + 700 + 500 = 2075 cm² Finally, multiply by 2: 2 × 2075…
    Full step-by-step solution

    Step 1: Calculate the volume using V = l × w × h V = 35 × 25 × 20 V = 875 × 20 V = 17500 cm³ Step 2: Calculate the surface area using SA = 2(lw + lh + wh) First, lw = 35 × 25 = 875 cm² Next, lh = 35 × 20 = 700 cm² Then, wh = 25 × 20 = 500 cm² Now add: 875 + 700 + 500 = 2075 cm² Finally, multiply by 2: 2 × 2075 = 4150 cm² The volume is 17500 cm³ and the surface area is 4150 cm².

  3. A rectangular prism has length 15 cm, width 10 cm, and height 8 cm. Calculate its volume and surface area. (Format: Volume = ? cm³, Surface Area = ? cm²) Answer: Volume = 1200 cm³, Surface Area = 700 cm² Solution: Calculate the volume using the formula: Volume = length × width × height Volume = 15 cm × 10 cm × 8 cm = 1200 cm³ Calculate the surface area using the formula: Surface Area = 2(lw + lh + wh) - lw = 15 × 10 = 150 cm² - lh = 15 × 8 = 120 cm² - wh = 10 × 8 = 80 cm² Sum these areas: 150 + 120 + 80 =…
    Full step-by-step solution

    Step 1: Calculate the volume using the formula: Volume = length × width × height Volume = 15 cm × 10 cm × 8 cm = 1200 cm³ Step 2: Calculate the surface area using the formula: Surface Area = 2(lw + lh + wh) First, calculate each face area: - lw = 15 × 10 = 150 cm² - lh = 15 × 8 = 120 cm² - wh = 10 × 8 = 80 cm² Step 3: Sum these areas: 150 + 120 + 80 = 350 cm² Step 4: Multiply by 2 to get total surface area: 2 × 350 = 700 cm² Final answer: Volume = 1200 cm³, Surface Area = 700 cm²

  4. Mason is designing a cylindrical storage tank for his family's rainwater collection system. The tank needs to hold exactly 17,000 liters of water and has a height of 2.7 meters. What is the radius of the tank's circular base? Use π ≈ 3.14 and round your answer to the nearest tenth of a meter. (Remember: 1 cubic meter = 1000 liters) Answer: 1.4 Solution: Convert 17,000 liters to cubic meters. Since 1 cubic meter = 1000 liters, 17,000 liters = 17,000 / 1000 = 17 cubic meters. Use the volume formula for a cylinder: V = πr²h.
    Full step-by-step solution

    Step 1: Convert 17,000 liters to cubic meters. Since 1 cubic meter = 1000 liters, 17,000 liters = 17,000 / 1000 = 17 cubic meters. Step 2: Use the volume formula for a cylinder: V = πr²h. Here V = 17 m³, h = 2.7 m, and π = 3.14. Step 3: Substitute into the formula: 17 = 3.14 × r² × 2.7 Step 4: Multiply 3.14 by 2.7: 3.14 × 2.7 = 8.478 Step 5: So 17 = 8.478 × r² Step 6: Divide both sides by 8.478: r² = 17 / 8.478 ≈ 2.005 Step 7: Take the square root of both sides: r = sqrt(2.005) ≈ 1.416 Step 8: Round to the nearest tenth: r ≈ 1.4 meters The answer is 1.4.