Pythagorean 3D Worksheets Grade 8

1. Mere is building a display case for a museum artifact. The case is a rectangular prism with a length of 8 cm, a width of 6 cm, and a height of 4 cm. She wants to place a laser pointer at the bottom front left corner so that the beam travels in a straight line to the top back right corner of the case. What is the length, in centimeters, of the laser beam's path through the case?
2. A rectangular prism has dimensions 6 cm × 8 cm × 24 cm. Find the length of the space diagonal from one vertex to the opposite vertex.
3. √(9² + 12² + 20²) = ?

…and 2 more problems

1. A rectangular box has dimensions of 6 cm by 8 cm by 10 cm. What is the length of the space diagonal that runs from one corner of the box to the opposite corner?
2. Aroha is designing a large rectangular display case for a museum exhibit. The case has interior dimensions of 14 cm long, 11 cm wide, and 9 cm high. She wants to place a straight metal rod from the bottom front left corner to the top back right corner of the case to support a hanging artifact. What is the length of the longest rod that can fit in a straight line inside the case? Round your answer to the nearest tenth of a centimeter.
3. A rectangular prism has dimensions of 6 cm by 8 cm by 10 cm. A spider needs to travel from one corner of the prism to the opposite corner along the shortest possible path on the surface. What is the length of this shortest path?

…and 2 more problems

1. Sophia is helping her school's drama club build a set for an upcoming play. They are constructing a large rectangular storage box to hold props backstage. The interior dimensions of the box are 18 feet long, 15 feet wide, and 12 feet high. Sophia needs to place a long, straight decorative pole diagonally from the bottom front left corner of the box to the top back right corner. What is the exact length of the longest pole that can fit in a straight line inside the box?
2. Emma is building a model of a tower for her school project. The tower is shaped like a rectangular prism with a base that is 7 cm long and 5 cm wide, and a height of 11 cm. She wants to run a thin wire from the bottom front left corner of the tower to the top back right corner, going straight through the interior. What is the exact length of the wire she needs?
3. √(11² + 60² + 61²) = ?

…and 1 more problems