pre algebra - Pythagorean Theorem in Three Dimensions

Use the diagonal of the face of the cube and the side length of the cube to find the length of the diagonal of the cube. Round to the nearest tenth of an inch.

10.4

Jorge needs to ship a thin metal rod to a metalworking shop. The only boxes available for shipping are 7-inch cubes. To the nearest inch, what is the length of the longest metal rod that can be sent?

12

bc is 10 inches long, and ab is 300 inches long. What is the length of ac?

200 in.

What are the exact lengths of BC and CF?

242 and 363

A diagonal of a cube measures 294 cm. The diagonal of a face measures 14 cm. What is the length of an edge of the cube? Round to the nearest tenth of a centimeter.

9.9 cm

Which line segment is not a diagonal through the interior of the cube shown?

CE

Micaela has a bat that is 30 inches long. She wants to fit it in a cube shaped box that has sides that are 17 inches. Will the bat fit? Justify your answer.

No, the bat will not fit. Using the Pythagorean theorem, the length of a diagonal of a face of the box is about 24 inches, and the length of the diagonal of the cube is about 29.4 inches. This is less than the length of the bat.

The line segments of a cube include edges, the diagonals of the faces, and the diagonals through the interior of the cube. Which is the longest? Which is the shortest? Explain.

The diagonal through the interior of the cube is the longest. The hypotenuse is the longest side of a right triangle. The diagonal of the cube is the hypotenuse of a right triangle with legs that are the diagonal of a face and an edge. The edges are the shortest. They are legs of a right triangle with the diagonal of a face as the hypotenuse.

Which are right triangles that can be formed using a diagonal through the interior of the cube? Select all that apply.

b, c, e, f