Skills · Trigonometry · Right Triangles & Trigonometry

The Pythagorean theorem in 3D

Printable practice with an answer key the engine computes, at three levels, in as many versions as you need.

Problem types

Sample Sheet · Level 1

  1. a square pyramid with base edge 40, height 15 and slant height ?4015?
    Find the pyramid’s slant height.
  2. a cone with radius 15, height 8 and slant height ?158?
    Find the cone’s slant height.
  3. a square pyramid with base edge 20, height 24 and slant height ?2024?
    Find the pyramid’s slant height.
  4. a cone with radius 12, height 16 and slant height ?1216?
    Find the cone’s slant height.
  5. a square pyramid with base edge 18, height 12 and slant height ?1812?
    Find the pyramid’s slant height.
  6. a cone with radius 6, height 8 and slant height ?68?
    Find the cone’s slant height.
  7. a square pyramid with base edge 6, height 4 and slant height ?64?
    Find the pyramid’s slant height.
  8. a cone with radius 24, height 18 and slant height ?2418?
    Find the cone’s slant height.

Answer key

  1. 25 units
  2. 17 units
  3. 26 units
  4. 20 units
  5. 15 units
  6. 10 units
  7. 5 units
  8. 30 units

Sample Sheet · Level 3

  1. a box 4 by 2 by 4, its diagonal ?442?
    Find the length of the box’s diagonal.
  2. a square pyramid with base edge 6, height 4 and slant height ?64?
    Find the pyramid’s slant height.
  3. a cone with radius 18, height 24 and slant height ?1824?
    Find the cone’s slant height.
  4. a cone with radius 9, height ? and slant height 159?15
    Find the cone’s height.
  5. a square pyramid with base edge 30, height 8 and slant height ?308?
    Find the pyramid’s slant height.
  6. a cone with radius 15, height ? and slant height 1715?17
    Find the cone’s height.
  7. a cone with radius 10, height 24 and slant height ?1024?
    Find the cone’s slant height.
  8. a box 14 by 7 by 14, its diagonal ?14147?
    Find the length of the box’s diagonal.

Answer key

  1. 6 units
  2. 5 units
  3. 30 units
  4. 12 units
  5. 17 units
  6. 8 units
  7. 26 units
  8. 21 units

Make your own

Pick the count, the level and the version, and print it with work space and the key on its own page. The same skill also makes an I Do, We Do, You Do lesson, a Mosaic, a Decoder and more.

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