10.1.3 Formulas in Three Dimensions − Practice
1. Identify the number of vertices, edges, and faces of the polyhedron. Use your results to verify Euler’s formula.
2. The diagonal of a cube is 20 cm. Find the length of an edge. Round to the nearest tenth, if necessary.
3. A rectangular prism has a base of 18 cm by 15 cm and a diagonal of 25 cm. Find its height. Round to the nearest tenth.
4. A rectangular prism has a base of 19 ft by 8 ft and a diagonal of 25 ft. Find its height. Round to the nearest tenth.
5. Find the distance between points ( − 1, 7, 10) and (6, − 3, 2), and find the
6. Two people meet in the purple room on the fourth floor of a building. On departure, one person travels West 20 feet, South 12 feet, and Down 12 feet. The other person travels North 20 feet, East 10 feet, and Up 12 feet. How far apart are the two people? Round to the nearest tenth.
midpoint of the segment for which these are the endpoints. Round to the nearest tenth, if necessary.
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