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Area and Surface Formulas

Grade 7 · Geometry · Worksheet 2

  1. Hana is designing a cylindrical water feature for a community park. The cylinder will have a radius of 1.5 meters and a height of 2.8 meters. She needs to paint the curved surface and the two circular ends (top and bottom) with a special waterproof sealant. What is the total surface area Hana needs to cover, in square meters? Use pi = 3.14 and round your answer to the nearest whole number.
    Answer: ______________
  2. A cylinder has a radius of 8 cm and a height of 14 cm. Calculate its total surface area. Use π = 3.14.
    Answer: ______________
  3. A rectangular prism has length 12 cm, width 8 cm, and height 6 cm. Calculate its surface area.
    Answer: ______________
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Answer Key & Explanations

Area and Surface Formulas · Grade 7 · Worksheet 2

  1. Hana is designing a cylindrical water feature for a community park. The cylinder will have a radius of 1.5 meters and a height of 2.8 meters. She needs to paint the curved surface and the two circular ends (top and bottom) with a special waterproof sealant. What is the total surface area Hana needs to cover, in square meters? Use pi = 3.14 and round your answer to the nearest whole number. Answer: 41 Solution: Find the area of the two circular ends. Area of one circle = pi * r^2 = 3.14 * (1.5)^2 = 3.14 * 2.25 = 7.065 square meters. Two circles = 2 * 7.065 = 14.13 square meters.
    Full step-by-step solution

    Step 1: Find the area of the two circular ends. Area of one circle = pi * r^2 = 3.14 * (1.5)^2 = 3.14 * 2.25 = 7.065 square meters. Two circles = 2 * 7.065 = 14.13 square meters. Step 2: Find the curved surface area. The curved surface is a rectangle when unrolled. Its width is the circumference of the circle = 2 * pi * r = 2 * 3.14 * 1.5 = 9.42 meters. Its height is the cylinder's height = 2.8 meters. Area = 9.42 * 2.8 = 26.376 square meters. Step 3: Add the areas together: 14.13 + 26.376 = 40.506 square meters. Step 4: Round to the nearest whole number: 41 square meters. The total surface area is 41 square meters.

  2. A cylinder has a radius of 8 cm and a height of 14 cm. Calculate its total surface area. Use π = 3.14. Answer: 1105.28 Solution: Identify the formula for total surface area of a cylinder: SA = 2πr² + 2πrh Calculate the area of the two circular ends: 2πr² = 2 × 3.14 × 8² = 2 × 3.14 × 64 = 2 × 200.96 = 401.92 cm² Calculate the curved surface area: 2πrh = 2 × 3.14 × 8 × 14 = 2 × 3.14 × 112 = 2 × 351.68 = 703.36 cm² Add the…
    Full step-by-step solution

    Step 1: Identify the formula for total surface area of a cylinder: SA = 2πr² + 2πrh Step 2: Calculate the area of the two circular ends: 2πr² = 2 × 3.14 × 8² = 2 × 3.14 × 64 = 2 × 200.96 = 401.92 cm² Step 3: Calculate the curved surface area: 2πrh = 2 × 3.14 × 8 × 14 = 2 × 3.14 × 112 = 2 × 351.68 = 703.36 cm² Step 4: Add the two parts: 401.92 + 703.36 = 1105.28 cm² The total surface area is 1105.28 cm².

  3. A rectangular prism has length 12 cm, width 8 cm, and height 6 cm. Calculate its surface area. Answer: 432 Solution: Identify the formula for surface area of a rectangular prism: SA = 2lw + 2lh + 2wh Substitute the given dimensions: l = 12 cm, w = 8 cm, h = 6 cm Calculate 2lw = 2 × 12 × 8 = 192 Calculate 2lh = 2 × 12 × 6 = 144 Calculate 2wh = 2 × 8 × 6 = 96 Add all three results: 192 + 144 + 96 = 432 Include…
    Full step-by-step solution

    Step 1: Identify the formula for surface area of a rectangular prism: SA = 2lw + 2lh + 2wh Step 2: Substitute the given dimensions: l = 12 cm, w = 8 cm, h = 6 cm Step 3: Calculate 2lw = 2 × 12 × 8 = 192 Step 4: Calculate 2lh = 2 × 12 × 6 = 144 Step 5: Calculate 2wh = 2 × 8 × 6 = 96 Step 6: Add all three results: 192 + 144 + 96 = 432 Step 7: Include units: 432 cm² The surface area is 432 cm².