Pythagorean 3D Worksheets Grade 8

1. Maya is setting up a zip line between two trees in her backyard. The horizontal distance between the trees is 15 meters, and the height difference between the attachment points is 8 meters. If the zip line cable needs to be 2 meters longer than the direct diagonal distance to allow for sag and attachment, what total length of cable should Maya purchase? Round your answer to the nearest tenth of a meter.
2. Sophia is helping her school's drama club build a large rectangular storage trunk for costumes. The interior of the trunk is 30 cm long, 24 cm wide, and 18 cm high. She wants to place a straight metal rod from the bottom front left corner to the top back right corner of the trunk to use as a support for hanging costumes. What is the exact length, in centimeters, of the longest straight metal rod that can fit inside the trunk? Simplify the square root if possible.
3. A rectangular prism 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 prism to the opposite corner? Round your answer to the nearest tenth of a centimeter.

…and 3 more problems

1. Liam is building a triangular support brace for his bookshelf. The brace needs to fit diagonally across the back of the shelf, which is 24 inches wide and 18 inches tall. What is the exact length of the diagonal brace Liam needs to cut?
2. A rectangular prism has dimensions 11 cm × 16 cm × 26 cm. Find the length of the space diagonal from one vertex to the opposite vertex.
3. 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?

…and 1 more problems

1. A rectangular pyramid has a base measuring 12 cm by 16 cm and a vertical height of 15 cm from the center of the base to the apex. What is the length of the slant edge from the apex to one of the base's corners? Round your answer to the nearest tenth of a centimeter.
2. Kaia has a rectangular storage shed. The floor is 7 feet by 9 feet, and the vertical height from the floor to the ceiling is 11 feet. A support cable runs in a straight line from the bottom front left corner of the floor to the top back right corner of the ceiling. What is the length of this cable? Round your answer to the nearest tenth of a foot.
3. Emma is designing a large art installation in the shape of a rectangular prism. The base of the prism is 15 feet long and 20 feet wide. The height of the prism is 25 feet. A support cable runs in a straight line from the bottom front left corner of the prism to the top back right corner. What is the length of this support cable, to the nearest foot?

…and 1 more problems