Spatial Reasoning Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
A rectangular box is 66 cm long, 44 cm wide, and 33 cm tall. What is the length of the space diagonal (corner to opposite corner)?

Solution

  1. 1
    Step 1: The space diagonal of a box with dimensions l,w,hl, w, h is d=l2+w2+h2d = \sqrt{l^2 + w^2 + h^2}.
  2. 2
    Step 2: d=62+42+32=36+16+9=61≈7.81d = \sqrt{6^2 + 4^2 + 3^2} = \sqrt{36 + 16 + 9} = \sqrt{61} \approx 7.81 cm.

Answer

d=61≈7.81d = \sqrt{61} \approx 7.81 cm.
The space diagonal extends through the interior of the box. Applying the Pythagorean theorem twice (first across the base, then up through the height) gives d=l2+w2+h2d = \sqrt{l^2+w^2+h^2}.

About Spatial Reasoning

The cognitive ability to visualize, manipulate, and reason about two- and three-dimensional objects mentally in space.

Learn more about Spatial Reasoning →

More Spatial Reasoning Examples

Example 1 easy

Look at this sequence of shapes: triangle, square, pentagon. How many sides does the next shape have

Example 2 medium

A cube is painted red on all 6 faces and then cut into [formula] smaller equal cubes. How many small

Example 3 easy

If you fold a square piece of paper in half and then in half again (both folds along the middle), ho

← All Spatial Reasoning Examples Spatial Reasoning Concept

Related Concepts

Function Transformation