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Area and Surface Formulas

Grade 7 · Geometry · Worksheet 1

  1. Emma is designing a circular fountain for a park. The fountain consists of a central circular pool with a radius of 5 meters, surrounded by a circular walkway that is 2 meters wide. The walkway will be made of decorative tiles. What is the total area of the walkway in square meters? (Use π = 3.14)
    Answer: ______________
  2. A cylinder has a radius of 14 cm and a height of 25 cm. Calculate its total surface area. (Use π = 22/7)
    Answer: ______________
  3. A rectangular prism has length 15 cm, width 8 cm, and height 6 cm. Calculate its surface area.
    Answer: ______________
  4. Liam is designing a cylindrical water tank for a community garden. The tank needs to hold exactly 12,000 liters of water and must have a height of 3 meters. What is the radius of the tank's base in meters? (Remember: 1 cubic meter = 1000 liters) Answer: ______________
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Answer Key & Explanations

Area and Surface Formulas · Grade 7 · Worksheet 1

  1. Emma is designing a circular fountain for a park. The fountain consists of a central circular pool with a radius of 5 meters, surrounded by a circular walkway that is 2 meters wide. The walkway will be made of decorative tiles. What is the total area of the walkway in square meters? (Use π = 3.14) Answer: 75.36 Solution: Identify the dimensions. The pool has a radius of 5 meters. The walkway is 2 meters wide, so the total radius from the center to the outer edge of the walkway is 5 + 2 = 7 meters.
    Full step-by-step solution

    Step 1: Identify the dimensions. The pool has a radius of 5 meters. The walkway is 2 meters wide, so the total radius from the center to the outer edge of the walkway is 5 + 2 = 7 meters. Step 2: Calculate the area of the pool (inner circle). Area of pool = π × r² = 3.14 × 5² = 3.14 × 25 = 78.5 square meters. Step 3: Calculate the area of the large circle (pool + walkway). Area of large circle = π × R² = 3.14 × 7² = 3.14 × 49 = 153.86 square meters. Step 4: Subtract to find the area of the walkway. Area of walkway = Area of large circle - Area of pool = 153.86 - 78.5 = 75.36 square meters. The answer is 75.36.

  2. A cylinder has a radius of 14 cm and a height of 25 cm. Calculate its total surface area. (Use π = 22/7) Answer: 3432 Solution: Identify the given values: radius r = 14 cm, height h = 25 cm, π = 22/7. Calculate the area of the two circular ends. Area of one circle = πr² = (22/7) × 14² = (22/7) × 196 = 22 × 28 = 616 cm².
    Full step-by-step solution

    Step 1: Identify the given values: radius r = 14 cm, height h = 25 cm, π = 22/7. Step 2: Calculate the area of the two circular ends. Area of one circle = πr² = (22/7) × 14² = (22/7) × 196 = 22 × 28 = 616 cm². Two circles: 2 × 616 = 1232 cm². Step 3: Calculate the curved surface area. Curved surface area = 2πrh = 2 × (22/7) × 14 × 25 = 2 × 22 × 2 × 25 = 44 × 50 = 2200 cm². Step 4: Add the areas together: total surface area = 1232 + 2200 = 3432 cm². The total surface area is 3432 cm².

  3. A rectangular prism has length 15 cm, width 8 cm, and height 6 cm. Calculate its surface area. Answer: 516 cm² Solution: Identify the three pairs of identical faces: length×width, length×height, and width×height Calculate area of length×width face: 15 × 8 = 120 cm² Calculate area of length×height face: 15 × 6 = 90 cm² Calculate area of width×height face: 8 × 6 = 48 cm² Add all six faces: 2 × (120 + 90 + 48) = 2 ×…
    Full step-by-step solution

    Step 1: Identify the three pairs of identical faces: length×width, length×height, and width×height Step 2: Calculate area of length×width face: 15 × 8 = 120 cm² Step 3: Calculate area of length×height face: 15 × 6 = 90 cm² Step 4: Calculate area of width×height face: 8 × 6 = 48 cm² Step 5: Add all six faces: 2 × (120 + 90 + 48) = 2 × 258 = 516 cm² Step 6: The surface area is 516 cm².

  4. Liam is designing a cylindrical water tank for a community garden. The tank needs to hold exactly 12,000 liters of water and must have a height of 3 meters. What is the radius of the tank's base in meters? (Remember: 1 cubic meter = 1000 liters) Answer: 1.13 Solution: - Volume = 12,000 liters - Height = 3 meters We need the radius in meters. Also, 1 cubic meter = 1000 liters. Volume in liters = 12,000 liters Since 1 m³ = 1000 liters, Volume in m³ = 12,000 / 1000 = 12 m³.
    Full step-by-step solution

    Step 1: Understand the problem We are told the tank is a cylinder with: - Volume = 12,000 liters - Height = 3 meters We need the radius in meters. Also, 1 cubic meter = 1000 liters. Step 2: Convert volume to cubic meters Volume in liters = 12,000 liters Since 1 m³ = 1000 liters, Volume in m³ = 12,000 / 1000 = 12 m³. Step 3: Recall the volume formula for a cylinder Volume of cylinder = π × r² × h Where: r = radius of base (in meters) h = height (in meters) π ≈ 3.1416 We know: Volume = 12 m³ Height h = 3 m So: π × r² × 3 = 12 Step 4: Solve for r² Divide both sides by 3: π × r² = 12 / 3 π × r² = 4 Now divide both sides by π: r² = 4 / π Step 5: Calculate r² Using π ≈ 3.1416: r² = 4 / 3.1416 ≈ 1.2732 Step 6: Find r r = square root of 1.2732 r ≈ 1.128 meters Step 7: Round to two decimal places 1.128 rounds to 1.13 meters. Final Answer: The radius of the tank's base is 1.13 meters.