# Cuboid + third power - examples

A cuboid is a three-dimensional shape with a length, width, and a height. A cuboid is a rectangular Prism. The cuboid shape has six sides called faces. Each face of a cuboid is a rectangle, and all of a cuboid's corners (called vertices) are 90-degree angles. Opposite faces are parallel. A cuboid has the shape of a rectangular box.

1. Prism X
The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm3. What is the area of surface of the prism?
2. Cuboids in cube
How many cuboids with dimensions of 6 cm, 8 cm and 12 cm can fit into a cube with side 96 centimeters?
3. Rectangle pool
Determine dimensions of open pool with a square bottom with a capacity 32 m3 to have painted/bricked walls with least amount of material.
4. Cuboid edges in ratio
Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm3.
5. Body diagonal
The cuboid has a volume of 32 cm3. Its side surface area is double as one of the square bases. What is the length of the body diagonal?
6. Volume and body diagonal
Calculate how much the volume and body diagonal of the cuboid decrease if we reduce each of its three edges a, b, c by 18%?
7. Minimum surface
Find the length, breadth, and height of the cuboid shaped box with a minimum surface area, into which 50 cuboid shaped blocks, each with length, breadth and height equal to 4 cm, 3 cm and 2 cm respectively can be packed.

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