Geometry Problem Solver

Cone and pyramid together

cone	pyramid

Cone 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 cone and pyramid together, are about 2 x 80 problems on cone x 200 problems on pyramid = 32,000

Track 1

The base circumference of a cone measures 36 π cm and the total area of the cone is 864 π cm². Calculates the height of a pyramid having a volume equal to 1/3 of the volume of the cone and the base area of 904.77792 cm².

Track 2

The base circumference of a cone measures 36 π cm and the total area of the cone is 864 π cm². Calculates the base area of a quadrangular pyramid equivalent to the cone and having a height congruent to 2/9 of the diameter of the cone.

Track 3

The base circumference of a cone measures 36 π cm and the total area of the cone is 864 π cm². Calculates the base area of a quadrangular pyramid equivalent to the cone and having the height equal to the diameter of the cone.

Track 4

The base circumference of a cone measures 36 π cm and the total area of the cone is 864 π cm². Calculates the base area of a quadrangular pyramid equivalent to the cone and having the height equal to the radius of the cone.

Track 5

The base circumference of a cone measures 36 π cm and the total area of the cone is 864 π cm². Calculates the base area of a quadrangular pyramid equivalent to the cone and having the height congruent to the cone apothem.

Track 6

The base circumference of a cone measures 36 π cm and the total area of the cone is 864 π cm². Calculates the base area of a quadrangular pyramid equivalent to the cone and having a height equal to 2/3 of the cone apothem.

Track 7

The base circumference of a cone measures 36 π cm and the total area of the cone is 864 π cm². Calculates the volume of a quadrangular pyramid having the apothem equal to 13/15 of the cone apothem and the base side of 20 cm.

Track 8

The base circumference of a cone measures 36 π cm and the total area of the cone is 864 π cm². Calculates the volume of a pentagonal pyramid having the apothem equal to 13/15 of the cone apothem and the base side of 10 cm.

Track 9

The base circumference of a cone measures 36 π cm and the total area of the cone is 864 π cm². Calculates the volume of a hexagonal pyramid with apothem equal to 13/15 of the cone apothem and the base side of 10 cm.

Track 10

The base circumference of a cone measures 36 π cm and the total area of the cone is 864 π cm². Calculates the volume of a rectangular pyramid whose base dimensions measure respectively 24 cm and 18 cm and have the height congruent to 13/15 of the cone apothem.

Track 11

The base circumference of a cone measures 36 π cm and the total area of the cone is 864 π cm². 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 5/3 of the height of the cone.

Track 12

The base circumference of a cone measures 36 π cm and the total area of the cone is 864 π cm². Calculates the volume of a pentagonal pyramid with the same lateral area of the cone and the apothem equal to 13/15 of the cone apothem.

Track 13

The base circumference of a cone measures 36 π cm and the total area of the cone is 2714.3338 cm². Calculates the volume of a pyramid with the same total area of the cone and the base area congruent to 13/15 of the base area of the cone.

Track 14

A quadrangular pyramid has a base edge of 20 cm and a height of 24 cm. Calculates the height of a cone congruent to the pyramid and having the basic circumference equal to 5/3 of the pyramid apothem.

Track 15

A pentagonal pyramid has a base edge of 20 cm and a height of 24 cm. Calculates the height of a cone congruent to the pyramid and having the basic circumference equal to 5/2 of the pyramid apothem.

Track 16

A rhomboid pyramid has long base diagonals respectively of 40 cm and 30 cm; Has a height of 16 cm. Calculates the height of a cone congruent to the pyramid and having the basic circumference equal to 5/2 of the pyramid apothem.

Track 17

A pyramid has as base a rectangular triangle with a 150 cm² area and a 15 cm lower cathetus; Has a height of 12 cm. Calculates the height of a cone congruent to the pyramid and having the basic circumference equal to 20/13 of the pyramid apothem.

Track 18

A pyramid has as base a rectangle, whose base dimensions are respectively of 24 cm and 18 cm; Has a height of 40 cm. Calculates the height of a cone congruent to the pyramid and having the base area equal to 5/2 of the base area of the pyramid.

Track 19

The base circumference of a cone measures 36 π cm and the total area of the cone is 864 π cm². Calculates the volume of a rhomboidal pyramid with a base area of 500 cm² and a height equal to 3/4 of the height of the cone.

Cone alone

Pyramid alone