Cube cut

In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.

Result

r =  1:4

Solution:

Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

To solve this example are needed these knowledge from mathematics:

Need help calculate sum, simplify or multiply fractions? Try our fraction calculator. See also our right triangle calculator. Tip: Our volume units converter will help you with converion of volume units. See also our trigonometric triangle calculator.

Next similar examples:

1. Transforming cuboid
Cuboid with dimensions 8 cm, 13, and 16 cm is converted into a cube with the same volume. What is its edge length?
2. Cube in a sphere
The cube is inscribed in a sphere with volume 6116 cm3. Determine the length of the edges of a cube.
3. Cubes
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
4. TV transmitter
The volume of water in the rectangular swimming pool is 6998.4 hectoliters. The promotional leaflet states that if we wanted all the pool water to flow into a regular quadrangle with a base edge equal to the average depth of the pool, the prism would have.
5. Cuboid
Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm3. Calculate the length of the other edges.
6. Pool
The swimming pool is 10 m wide and 8 m long and 153 cm deep. How many hectoliters of water is in it, if the water is 30 cm below its upper edge?
7. Pool
If water flows into the pool by two inlets, fill the whole for 8 hours. The first inlet filled pool 6 hour longer than second. How long pool take to fill with two inlets separately?
8. Ratio of volumes
If the heights of two cylindrical drums are in the ratio 7:8 and their base radii are in the ratio 4:3. What is the ratio of their volumes?
9. Three tributaries
It is possible to fill the pool with three tributaries. The first would take 12 hours, the second 15 hours, and the third 20 hours. The day before the summer season began, the manager opened all three tributaries simultaneously. How long did it take to fil
10. Lateral surface area
The ratio of the area of the base of the rotary cone to its lateral surface area is 3: 5. Calculate the surface and volume of the cone, if its height v = 4 cm.
11. Sphere VS
Find the surface and volume of a sphere that has a radius of 2 dm.
The text passage contains a mathematical question related to the division of a cube by a plane and the ratio in which an edge is divided by this plane. An answer to this question is also provided.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Cube cut

In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.

Result

r =  1:4

Solution:

Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

To solve this example are needed these knowledge from mathematics:

Need help calculate sum, simplify or multiply fractions? Try our fraction calculator. See also our right triangle calculator. Tip: Our volume units converter will help you with converion of volume units. See also our trigonometric triangle calculator.

Next similar examples:

1. Transforming cuboid
Cuboid with dimensions 8 cm, 13, and 16 cm is converted into a cube with the same volume. What is its edge length?
2. Cube in a sphere
The cube is inscribed in a sphere with volume 6116 cm3. Determine the length of the edges of a cube.
3. Cubes
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
4. TV transmitter
The volume of water in the rectangular swimming pool is 6998.4 hectoliters. The promotional leaflet states that if we wanted all the pool water to flow into a regular quadrangle with a base edge equal to the average depth of the pool, the prism would have.
5. Cuboid
Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm3. Calculate the length of the other edges.
6. Pool
The swimming pool is 10 m wide and 8 m long and 153 cm deep. How many hectoliters of water is in it, if the water is 30 cm below its upper edge?
7. Pool
If water flows into the pool by two inlets, fill the whole for 8 hours. The first inlet filled pool 6 hour longer than second. How long pool take to fill with two inlets separately?
8. Ratio of volumes
If the heights of two cylindrical drums are in the ratio 7:8 and their base radii are in the ratio 4:3. What is the ratio of their volumes?
9. Three tributaries
It is possible to fill the pool with three tributaries. The first would take 12 hours, the second 15 hours, and the third 20 hours. The day before the summer season began, the manager opened all three tributaries simultaneously. How long did it take to fil
10. Lateral surface area
The ratio of the area of the base of the rotary cone to its lateral surface area is 3: 5. Calculate the surface and volume of the cone, if its height v = 4 cm.
11. Sphere VS
Find the surface and volume of a sphere that has a radius of 2 dm.
user
The text passage contains a mathematical question related to the division of a cube by a plane and the ratio in which an edge is divided by this plane. An answer to this question is also provided.

TYPE: SINGLE_QUESTION_WITH_ANSWER