Find the volume of the largest right circular cone that can be cut out of cube having 5 cm as its length of the side.

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A21.82

B45.67

C32.72

D65.45

Answer:

A right circular cone is a three-dimensional geometric shape with a circular base and a vertex that is directly above the center of the base.
A cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

To cut the largest possible right circular cone from a cube, the cone's base must be inscribed within one of the cube's faces, and the cone's height must be equal to the cube's side length.
Diameter of the Cone's Base: The diameter of the largest circle that can be inscribed in a square face of the cube will be equal to the side length of the cube.
Radius of the Cone's Base (r): If the side length of the cube is 'a', then the diameter of the cone's base is 'a'. Therefore, the radius (r) = a/2.
Height of the Cone (h): The maximum height the cone can have within the cube is equal to the side length of the cube, so h = a.

The volume (V) of a right circular cone is given by the formula: V = (1/3) * "π" * r^2 * h
Where 'r' is the radius of the base and 'h' is the height of the cone.

Using the approximate value of "π" â‰ˆ 3.14159
V â‰ˆ (125/12) * 3.14159
V â‰ˆ 10.4167 * 3.14159
V â‰ˆ 32.7249...
Rounding to two decimal places, the volume is approximately 32.72 cubic centimeters.

Key Ratios: Always remember that for the largest cone in a cube, the radius is half the side length, and the height is equal to the side length.
Formula Recall: Be quick to recall the volume of a cone formula.
Approximation: For MCQs, often you can estimate "π" as 22/7 or 3.14 to quickly narrow down options if exact calculation isn't needed.
Units: Ensure the final answer includes the correct cubic units (e.g., cmÂ³).

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