Geometry Problem Solver

Cube and pyramid together

Cube	pyramid

Cube alone

Pyramid alone

They give the tracks some problems can be solved automatically, the numerical values do not matter in the various examples. Only the problems already tested are reported. In fact, the problems solved by the geometric computer, but not tested, with a cube and pyramid together, are about 2 x 7 problems on cube x 200 problems on pyramid = 14,000

Track 1

A solid is the sum between a cube and a quadrangular pyramid with the base edges coinciding with the edges of a cube face. Knowing that the face area is 784 cm² and that the surface area of the solid is 6720 cm², it calculates the height of the pyramid and the volume.

Track 2

A regular quadrangular pyramid is equivalent to a cube, with a total surface area of 600 cm². Knowing that the height of the pyramid is 7.5 cm, it calculates the total surface area.

Track 3

A quadrangular regular pyramid has a volume of 10368 cm³ and a height of 24 cm. Calculates: 1) the apothem of the pyramid; 2) the lateral area of a cube that has the edge congruent to the pyramid apothem.

Track 4

A solid is formed of two overlapping and concentric cubes. The edges measure 10 cm and 5 cm. Calculates:
- The total area of the solid;
- The height of a rectangular pyramid equivalent to the solid and having a basis congruent to that of the major cube.

Track 5

A rhomboid pyramid has long base diagonals respectively of 40 cm and 30 cm; Has a height of 16 cm. Calculates the diagonal of a cube congruent to the pyramid.

Track 6

A rhomboid pyramid has long base diagonals respectively of 40 cm and 30 cm; Has a height of 16 cm. Calculates the diagonal of a congruent cube to 1/4 of the pyramid.

Track 7

A cube has a 10 cm edge. Calculates the height of a congruent rhomboid pyramid at 3/2 of the cube and having the base area congruent to 3/4 of the lateral area of the cube.

Track 8

A rhomboid pyramid has long base diagonals respectively of 40 cm and 30 cm; Has a height of 16 cm. Calculates the volume of a cube with the edge congruent at the pyramid apothem.

Track 9

A rhomboid pyramid has long base diagonals respectively of 40 cm and 30 cm; Has a height of 16 cm. Calculates the volume of a cube with the edge congruent at 4/5 of the pyramid apothem.

Track 10

A rhomboid pyramid has long base diagonals respectively of 40 cm and 30 cm; Has the apothem of 20 cm. Calculates the volume of a cube with the diagonal congruent to 3/4 of the height of the pyramid.

Track 11

A cube has a volume of 1000 cm³. Calculates the total area of a pyramid that has a rectangular triangle with a 336 cm² area and a 14 cm long cathetus, knowing that the height of the pyramid is congruent to 4/5 of the cube edge.

Cube alone

Pyramid alone