An edge of a cube is r cm. If the largest possible right circular cone is cut…
2016
An edge of a cube is r cm. If the largest possible right circular cone is cut out of it, then the volume of the cone (in cm³) is
- A.
(1/6)πr³
- B.
(1/12)πr³
- C.
(1/3)πr³
- D.
(2/3)πr³
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Correct answer: B
To find the volume of the largest right circular cone cut out of a cube with edge length r, we determine the dimensions of the cone.
The base of the largest inscribed cone will have a diameter equal to the edge of the cube, so the radius is r/2.
The height of the cone will be equal to the edge of the cube, which is r.
Using the volume formula for a cone V = (1/3)π(radius)^2(height),
we substitute the values: V = (1/3)π(r/2)^2(r).
Simplifying this gives V = (1/3)π(r^2/4)(r) = (1/12)πr^3.