Question:
A cube is dissected by one plane at \( \frac{1}{6} \) side length and one plane at \( \frac{1}{2} \) side length in each of the three dimensions of \(xy\), \(yz\), and \(xz\). How many cubes will be formed after dissecting the large cube?
A cube is dissected by one plane at \( \frac{1}{6} \) side length and one plane at \( \frac{1}{2} \) side length in each of the three dimensions of \(xy\), \(yz\), and \(xz\). How many cubes will be formed after dissecting the large cube?
Show Hint
When dividing a 3D shape like a cube, each plane adds one division along that dimension. Multiply the number of divisions for all dimensions to get the total number of resulting shapes.
Updated On: Jan 13, 2026
Hide Solution
Verified By Collegedunia
Correct Answer: 3
Solution and Explanation
1. Each plane divides the cube into multiple sections along the given dimension.
2. With the given dimensions, the large cube is divided into 3 parts in total: one along \( \frac{1}{6} \), one along \( \frac{1}{2} \), and one remaining piece.
Conclusion: The cube is divided into 3 smaller cubes.
2. With the given dimensions, the large cube is divided into 3 parts in total: one along \( \frac{1}{6} \), one along \( \frac{1}{2} \), and one remaining piece.
Conclusion: The cube is divided into 3 smaller cubes.
Was this answer helpful?
0
0
Top Questions on Geometry
- If \( L_1 \) and \( L_2 \) are two parallel lines and \( \triangle ABC \) is an equilateral triangle as shown in the figure, then the area of triangle \( ABC \) is:
- The locus of the point of intersection of tangents drawn to the circle \[ (x - 2)^2 + (y - 3)^2 = 16, \] which subtends an angle of \(120^\circ\), is:
- If \( O \) is the vertex of the parabola \( x^2 = 4y \), \( Q \) is a point on the parabola. If \( C \) is the locus of a point which divides \( OQ \) in the ratio \( 2:3 \), then the equation of the chord of \( C \) which is bisected at the point \( (1,2) \) is:
- During Durga Puja, for the purpose of lighting, one puja pandal in Kolkata used many identical structures made of wooden sticks. The design of the structures was as follows: each structure was constructed with the help of six wooden sticks by combining an isosceles triangular structure, and a square structure, with the bases of both structures being the same. Let us take one such structure. Call the triangle PAB, with PA = PB, and the square ABCD, with AB being the same wooden stick as a common base for the triangle and the square. To make the structure strong, the two equal sides of the triangular structure were tied with the opposite side of square’s base, i.e., CD, at points E and F, in such a way that CE = EF = FD. The structure was hung from P.
If AB = 0.5m (meter), the total length of wooden sticks required for twenty such structures is:
- Ronny uses a 5-digit key for a combination lock, where 5 digits need to be entered in a fixed sequence. While he remembers that the 5 digits are 9, 8, 7, 5, and 4, he has forgotten the sequence he uses. He also remembers that the sum of the first three digits is a multiple of 3, and so is the sum of the last three digits. Further, the sum of the last four digits is a multiple of 4.
Which of the following is DEFINITELY FALSE?
View More Questions
Questions Asked in CEED exam
- When "Rule of thirds" is applied to a picture/image, then in how many parts the picture/image will be divided?
- CEED - 2026
- Design Problem Solving
- Ravi has a briefcase with dimensions of two by 1 ½ by 1 ½ feet. He wishes to place several notebooks, each eight by nine by one inch, into the briefcase. What is the largest number of notebooks the briefcase will hold?
- CEED - 2026
- Quantitative Aptitude
- In which country did Bauhaus -- the first formal design school -- was established?
- CEED - 2026
- Design Problem Solving
- Select the correct basic types of "perspective"
- CEED - 2026
- Drawing
- Which of the following is/ARE considered "Impossible triangle"?
- CEED - 2026
- Visual Perception
View More Questions