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3D Volume and Surface

Grade 7 · Geometry · Worksheet 3

  1. Emma has a rectangular prism with dimensions 40 cm × 25 cm × 35 cm. Calculate its volume and total surface area. (Format: Volume = ? cm³, Surface Area = ? cm²)
    Answer: ______________
  2. A rectangular prism has dimensions 30 cm × 20 cm × 15 cm. Calculate its volume and total surface area. (Format: Volume = ? cm³, Surface Area = ? cm²)
    Answer: ______________
  3. Mason is building a rectangular prism-shaped planter box out of concrete. The planter box has a length of 18 inches, a width of 14 inches, and a height of 22 inches. Mason wants to fill the entire box with soil, and then cover the outside surfaces (including the top) with a waterproof sealant. What is the volume of soil needed (in cubic inches), and what is the total surface area that needs sealant (in square inches)?
    Answer: ______________
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Answer Key & Explanations

3D Volume and Surface · Grade 7 · Worksheet 3

  1. Emma has a rectangular prism with dimensions 40 cm × 25 cm × 35 cm. Calculate its volume and total surface area. (Format: Volume = ? cm³, Surface Area = ? cm²) Answer: Volume = 35000 cm³, Surface Area = 6550 cm² Solution: Calculate the volume using V = l × w × h V = 40 × 25 × 35 V = 1000 × 35 V = 35000 cm³ Calculate the surface area using SA = 2(lw + lh + wh) First, find lw = 40 × 25 = 1000 cm² Next, find lh = 40 × 35 = 1400 cm² Then, find wh = 25 × 35 = 875 cm² Now add the three areas: 1000 + 1400 + 875 = 3275…
    Full step-by-step solution

    Step 1: Calculate the volume using V = l × w × h V = 40 × 25 × 35 V = 1000 × 35 V = 35000 cm³ Step 2: Calculate the surface area using SA = 2(lw + lh + wh) First, find lw = 40 × 25 = 1000 cm² Next, find lh = 40 × 35 = 1400 cm² Then, find wh = 25 × 35 = 875 cm² Now add the three areas: 1000 + 1400 + 875 = 3275 cm² Finally, multiply by 2: 2 × 3275 = 6550 cm² The volume is 35000 cm³ and the surface area is 6550 cm².

  2. A rectangular prism has dimensions 30 cm × 20 cm × 15 cm. Calculate its volume and total surface area. (Format: Volume = ? cm³, Surface Area = ? cm²) Answer: Volume = 9000 cm³, Surface Area = 2700 cm² Solution: Calculate the volume using V = l × w × h V = 30 × 20 × 15 V = 600 × 15 V = 9000 cm³ Calculate the surface area using SA = 2(lw + lh + wh) First, lw = 30 × 20 = 600 cm² Next, lh = 30 × 15 = 450 cm² Then, wh = 20 × 15 = 300 cm² Now add: 600 + 450 + 300 = 1350 cm² Finally, multiply by 2: 2 × 1350 =…
    Full step-by-step solution

    Step 1: Calculate the volume using V = l × w × h V = 30 × 20 × 15 V = 600 × 15 V = 9000 cm³ Step 2: Calculate the surface area using SA = 2(lw + lh + wh) First, lw = 30 × 20 = 600 cm² Next, lh = 30 × 15 = 450 cm² Then, wh = 20 × 15 = 300 cm² Now add: 600 + 450 + 300 = 1350 cm² Finally, multiply by 2: 2 × 1350 = 2700 cm² The volume is 9000 cm³ and the surface area is 2700 cm².

  3. Mason is building a rectangular prism-shaped planter box out of concrete. The planter box has a length of 18 inches, a width of 14 inches, and a height of 22 inches. Mason wants to fill the entire box with soil, and then cover the outside surfaces (including the top) with a waterproof sealant. What is the volume of soil needed (in cubic inches), and what is the total surface area that needs sealant (in square inches)? Answer: Volume: 5544 cubic inches, Surface Area: 1672 square inches Solution: Volume of a rectangular prism = length x width x height. Here length = 18 in, width = 14 in, height = 22 in. Volume = 18 x 14 x 22.
    Full step-by-step solution

    Step 1: Volume of a rectangular prism = length x width x height. Here length = 18 in, width = 14 in, height = 22 in. Volume = 18 x 14 x 22. First, 18 x 14 = 252. Then, 252 x 22 = 5544. So volume = 5544 cubic inches. Step 2: Surface area of a rectangular prism = 2lw + 2lh + 2wh. - Area of top and bottom: 2 x (18 x 14) = 2 x 252 = 504 sq in. - Area of front and back: 2 x (18 x 22) = 2 x 396 = 792 sq in. - Area of left and right sides: 2 x (14 x 22) = 2 x 308 = 616 sq in. Total surface area = 504 + 792 + 616 = 1672 square inches. Final answer: Volume = 5544 cubic inches, Surface Area = 1672 square inches.