The volume of a cube is 8 \text{ cm}^3 and is equal to the volume of a cuboid of length x, breadth y and height z, where x, y and z are natural numbers (x > y > z). Let n be the number of such cuboids with different dimensions. What is the value of n ?
- A. 1 ✓
- B. 2
- C. 3
- D. More than 3
Correct Answer: A. 1
Explanation
The volume of the cuboid is xyz = 8. For x, y, and z to be distinct natural numbers with x > y > z, the only possible factorization of 8 is 4 \times 2 \times 1. Thus, there is only n = 1 such cuboid.
Related questions on Mensuration
- A pendulum swings through an angle of 30° and its end describes an arc of length 55 cm. What is the length of the pendulum? (Take $\pi = 22/...
- A conical tent has an angle of 60° at the vertex. If the curved surface area is 100 m^2, then what is the volume of the tent?
- A right circular cone and a hemisphere have equal base and equal volume. What is the ratio of the height of the cone to the radius of the he...
- A wire is in the form of an equilateral triangle with an area of 36\sqrt{3} cm^2. If it is changed into a semicircle, then what is its r...
- Let the area of the largest possible square inscribed in a circle of unit radius be x. Let the area of the largest possible circle inscribed...