Geometry Problem Solver

Cone and cylinder together

cylinder	cone

Cone alone

Cylinder 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 cylinder together, are about 2 x 80 problems on cone x 80 problems on cylinder = 12,800

Track 1

The base circumference of a cone measures 36 π cm and the total area is 864 π cm². Calculates the radius of a cylinder equivalent to the cone and having a height congruent to 3/4 of the height of the cone.

Track 2

A solid is formed by a cylinder surmounted by a cone with the base coincident with the top of the cylinder. The base area is 314,159 cm²; The height of the cylinder is 50 cm; The height of the cone is 24 cm. Calculate the total area and solid volume. Knowing that the solid is brass (ps = 8.5 kg/dm³), calculate the weight of the solid.

Track 3

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

Track 4

The base circumference of a cone measures 36 π cm and the total area is 864 π cm². Calculates the diameter of a cylinder equivalent to the cone and having a height congruent to 1/3 of the height of the cone.

Track 5

The base circumference of a cone measures 36 π cm and the total area is 864 π cm². Calculates the diameter of a cylinder equivalent to the cone and having a height equal to 4/15 of the cone apothem.

Track 6

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

Track 7

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

Track 8

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

Track 9

A rotating solid is composed of a cylinder and a cone having a coincident base whose area is 400 pigreca cm². The cone and cylinder have the same volume. Calculate:
- a) the lateral area of the cylinder knowing it is 30 cm high;
- b) the lateral area of the cone knowing that the apothem is 25 cm; - c) The total area of the compound solid and its total volume;
- d) calculates the ratio between the heights of the cylinder and the cone.

Track 10

The base circumference of a cylinder is 36 π cm and the total cylinder area is 864 π cm². Calculates the height of a cone congruent to the cylinder and having the base circumference congruent to 3/5 of the cylinder circumference.

Cone alone

Cylinder alone