# Cutting cone

A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm.

### Correct answer:

Tips for related online calculators

Check out our ratio calculator.

Do you want to convert length units?

See also our trigonometric triangle calculator.

Do you want to convert length units?

See also our trigonometric triangle calculator.

#### You need to know the following knowledge to solve this word math problem:

**geometry**- similarity of triangles
**algebra**- expression of a variable from the formula
**solid geometry**- cone
- frustum
**planimetrics**- triangle
**basic functions**- ratio

#### Units of physical quantities:

#### Grade of the word problem:

We encourage you to watch this tutorial video on this math problem: video1

## Related math problems and questions:

- Cross-sections of a cone

Cone with base radius 16 cm and height 11 cm divide by parallel planes to base into three bodies. The planes divide the height of the cone into three equal parts. Determine the volume ratio of the maximum and minimum of the resulting body. - Cone

Circular cone of height 15 cm and volume 5699 cm³ is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut. - Maximum of volume

The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum? - Right circular cone

The volume of a right circular cone is 5 liters. Calculate the volume of the two parts into which the cone is divided by a plane parallel to the base, one-third of the way down from the vertex to the base. - Projection 3493

In axometry, construct a projection of an oblique circular cone with a base in a plane. Dimension is given by the stop triangle, we know the center of the base S, the radius of the base ra the top of the cone V, Triangle (6,7,6), S (2,0,4), V (-2,7,6), r - Equilateral cone

We pour so much water into a container that has the shape of an equilateral cone, the base of which has a radius r = 6 cm, that one-third of the volume of the cone is filled. How high will the water reach if we turn the cone upside down? - Transfers 67414

At the height of 80 cm above the road, a person transfers a stone weighing 2 kg parallel to it in a uniform motion along a path of 6 m in 10 s. With what power does it work? - Cone

Circular cone with height h = 29 dm and base radius r = 3 dm slice plane parallel to the base. Calculate the distance of the cone vertex from this plane, if solids have the same volume. - Calculate 8325

Calculate the area of a circular section given by an angle of 220 degrees if the circle's radius is 20cm. Round the result to cm^{2} - Sports students

There are 120 athletes, 48 volleyball players, and 72 handball players at the school with extended sports training. Is it possible to divide sports students into groups so that the number in each group is the same and expressed by the largest possible num - Golden ratio

Divide the line of length 14 cm into two sections so that the ratio of shorter to greater is the same as the ratio of the greater section to the whole length of the line. - 2x cone

Circular cone height 84 cm was cut plane parallel with base. Volume of these two small cones is the same. Calculate the height of the smaller cone. - A Ferris wheel

A Ferris wheel with a diameter of 100 feet makes five revolutions every 8 minutes. The base of the wheel is 4 feet above the ground. Your friend gets on at 3 PM sharp. a) Write an equation to express the height in feet of your friend at any given time in - Axial section

The axial section of the cylinder has a diagonal 31 cm long, and we know that the area of the side and the base area is in ratio 3:2. Calculate the height and radius of the cylinder base. - Cylindrical 70024

We should grind a cylindrical rod with a diameter of 6 cm and a length of 20 cm to form a conical rod of the same size and the same base diameter. What will be the volume of material removed? - Inner-circle 2902

The inner-circle with a radius of 3 cm should be removed from the circle with a radius of 7 cm. How much of the area of the large circle will be removed? Express result in percent. - Similar frustums

The upper and lower radii of a frustum of a right circular cone are 8 cm and 32 cm, respectively. If the altitude of the frustum is 10 cm, how far from the bottom base must a cutting plane be made to form two similar frustums?