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Math 10C

Math 10C · Worksheets

Surface area and volume

Ten questions of mixed difficulty, covering Surface area and volume. Print it, or work through it on screen — the answer key starts on its own page.

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Surface area and volume

Math 10C · maddyhelps.com

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Circle the best answer for each question. Show your work in the space provided.

  1. A sphere has radius 6 cm. Its volume is about

    1. a) 452 cm³
    2. b) 905 cm³
    3. c) 144 cm³
    4. d) 226 cm³

  2. A cone has radius 4 cm and slant height 9 cm. Its total surface area is about

    1. a) 163 cm²
    2. b) 50 cm²
    3. c) 226 cm²
    4. d) 113 cm²

  3. A solid is a cylinder of radius 2 cm and height 8 cm with a hemisphere of the same radius on top. Its volume is about

    1. a) 134 cm³
    2. b) 101 cm³
    3. c) 117 cm³
    4. d) 84 cm³

  4. The surface area of a cube with edge length 4 cm is

    1. a) 96 cm²
    2. b) 16 cm²
    3. c) 64 cm²
    4. d) 24 cm²

  5. A square-based pyramid has base edge 6 cm and height 10 cm. Its volume is

    1. a) 360 cm³
    2. b) 200 cm³
    3. c) 60 cm³
    4. d) 120 cm³

  6. The volume of a cylinder is

    1. a) ⅓πr²h
    2. b) 2πrh
    3. c) πr²
    4. d) πr²h

  7. A cylinder has radius 3 cm and height 10 cm. Its total surface area is about

    1. a) 94 cm²
    2. b) 283 cm²
    3. c) 188 cm²
    4. d) 245 cm²

  8. The volume of a rectangular prism 3 cm by 4 cm by 5 cm is

    1. a) 60 cm³
    2. b) 47 cm³
    3. c) 94 cm³
    4. d) 12 cm³

  9. The surface area of a sphere of radius 5 cm is about

    1. a) 79 cm²
    2. b) 314 cm²
    3. c) 524 cm²
    4. d) 157 cm²

  10. Surface area is measured in

    1. a) no units
    2. b) linear units
    3. c) square units
    4. d) cubic units

Answer key · Surface area and volume

Math 10C · maddyhelps.com

  1. b) 905 cm³ — V = (4/3)πr³ = (4/3)π(216) ≈ 905 cm³. Cubing the radius is the step to be careful with: 6³ is 216, not 18.
  2. a) 163 cm² — SA = πr² + πrs = π(16) + π(36) ≈ 50 + 113 ≈ 163 cm². The curved part uses the <b>slant</b> height, not the vertical height — if a question gives the vertical height you have to find the slant with Pythagoras first.
  3. c) 117 cm³ — Add the parts: cylinder π(4)(8) ≈ 100.5, hemisphere ½ × (4/3)π(8) ≈ 16.8, total ≈ 117 cm³. For a composite <i>volume</i> you always add; for a composite <i>surface area</i> you also have to remove the faces that are now joined.
  4. a) 96 cm² — A cube has six identical square faces, each 4 × 4 = 16 cm², so 6 × 16 = 96 cm². The answer 64 is the volume, and mixing the two up is the most common slip in this unit.
  5. d) 120 cm³ — V = ⅓ × base area × height = ⅓ × 36 × 10 = 120 cm³. The base area uses the base edge, not the slant height — those are different lengths and questions often give both.
  6. d) πr²h — A cylinder is a prism with a circular base, so it is base area times height, and the base area is πr². The second option is the curved surface area and the fourth is the volume of a cone.
  7. d) 245 cm² — Two circles plus the curved side: 2πr² + 2πrh = 2π(9) + 2π(30) = 56.5 + 188.5 ≈ 245 cm². Forgetting the two ends gives 188, which is the most common wrong answer here.
  8. a) 60 cm³ — Volume of a prism is the area of the base times the height: 3 × 4 × 5 = 60 cm³. Volume is always in cubic units, which is a free check on whether you have found the right thing.
  9. b) 314 cm² — SA = 4πr² = 4π(25) ≈ 314 cm². Conveniently, a sphere's surface area is exactly four times the area of its own great circle.
  10. c) square units — Area covers a surface, so it is measured in units squared. Volume fills a space, so it is units cubed. If your answer's units do not match what was asked for, the formula was wrong.