Volume and Surface Area of Cones, Spheres and Pyramids · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Pointy solids and their measures

Mathematics · Geometry · ages 15-16
Name ______________________   Date ____________

  1. A square pyramid has a base 6 cm by 6 cm and a perpendicular height of 9 cm. What is its volume in cm3?

    Answer: ______________

  2. A cone has radius 3 cm and perpendicular height 4 cm. Which height goes into its volume?

    • The perpendicular height
    • The slant height
    • The diameter

  3. Which formula gives the volume of a sphere?

    • One third pi r squared h
    • Pi r s
    • Four thirds pi r cubed

  4. A square pyramid has a base 5 cm by 5 cm and a perpendicular height of 6 cm. What is its volume in cm3?

    Answer: ______________

  5. A cone has radius 3 cm and slant height 5 cm. Take pi = 3.14. What is its curved surface area?

    • 47.1 cm2
    • 94.2 cm2
    • 28.26 cm2
    • 15.7 cm2

  6. A hemisphere sits on a cylinder with the same radius. Which faces end up hidden inside?

    • The curved face of the hemisphere
    • The bottom face of the cylinder
    • The flat face of the hemisphere and the top face of the cylinder

  7. A cone has radius 5 cm and perpendicular height 12 cm. What is its slant height in cm?

    Answer: ______________

  8. A cone has radius 6 cm and perpendicular height 8 cm. What is its slant height in cm?

    Answer: ______________

  9. A solid is a cylinder of radius 3 cm and height 5 cm with a hemisphere of radius 3 cm on top. Take pi as 3.14. What is the total volume in cm3?

    Answer: ______________

  10. A solid is a cylinder of radius 3 cm and height 4 cm with a hemisphere of radius 3 cm on top. Take pi = 3.14. What is the total volume in cm3?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Pointy solids and their measures W1-mt_s4K5YMBSzG-s1

  1. 108 · One third of 36 by 9 is 108.
  2. The perpendicular height · Volume stacks slices vertically, so it needs the shortest drop from tip to base.
  3. Four thirds pi r cubed · Spheres follow their own rule: four thirds pi r cubed.
  4. 50 · One third of 25 by 6 is 50.
  5. 47.1 cm2 · Pi by r by s = 3.14 by 3 by 5 = 47.1.
  6. The flat face of the hemisphere and the top face of the cylinder · The join buries exactly the two faces that touch.
  7. 13 · Radius, height, and slant form a 5-12-13 triangle.
  8. 10 · Radius, height, and slant form a 6-8-10 triangle.
  9. 197.82 · Cylinder 141.3 plus hemisphere 56.52 gives 197.82.
  10. 169.56 · Cylinder 113.04 plus hemisphere 56.52 gives 169.56.
Worksheet · LightMySky