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8th Grade Math (Math 8) · Chapter 11 · Lesson 11.5 · Printable PDF

The Pythagorean Theorem in Three Dimensions Worksheet with Answer Key

7 problems on the Pythagorean theorem in three dimensions: space diagonals of boxes, a cube from a face diagonal, a student's units mistake, a bubble in glass, taped boxes, a greenhouse, and a pyramid-topped garden post. 2 pages, with a worked answer key.

7 problems2 pagesanswer key
Printable The Pythagorean theorem in three dimensions worksheet with answer key - 8th Grade Math (Math 8) (Page 1 PDF preview)
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What's on the worksheet

  1. Find the fourth measurement of a box from three of its length, width, height and space diagonal:
    l = 4, w = 4, h = 2l = 2, w = 10, h = 11l = 6, w = 6, h = 7l = 8, w = 9, h = 12l = 12, w = 4, d = 13
  2. Find the edge and the space diagonal of a cube from the diagonal of a face.
  3. Find the mistake in a student's work on a box's diagonal with mixed units.
  4. Word problem: how far an air bubble at the center of a glass block is from a corner.
  5. Compare how much tape two boxes with the same total edge length need.
  6. Word problem: the longest straight bar that fits in a box-shaped greenhouse frame.
  7. Word problem: the height of a stone post's pyramid from its slant height.

Teach it first

The free lesson teaches it with worked examples and practice problems.

The Pythagorean theorem in three dimensions: the lesson ›

More Chapter 11 worksheets: The Pythagorean theorem and distance